On Monday, Djokovic celebrated a 378th week as the best player in men's tennis, which overtook the all-time record (for men or women) set by Graf.
Like Graf, Djokovic has won 22 grand slam titles, though the 35-year-old remains in the hunt for more glory.
After his Australian Open triumph earlier this season, Djokovic will be hoping a 94th ATP Tour-level title comes his way at this week's Dubai Tennis Championships.
"I still want more achievements," Djokovic said ahead of breaking Graf's record.
"I could not have imagined this, I was dreaming as a kid to be Wimbledon champion, to be number one in the world. I achieved those dreams in 2011.
"After that, I wanted more. Of course, I'm driven by the goals. I'm as dedicated to the sport really as anybody else.
"It's surreal in a way to be that many weeks at world number one, to match Steffi Graf, who is one of the all-time greats of our sport. Just being among these legendary names is flattering. I'm very proud."
Djokovic's campaign in Dubai starts against Tomas Machac on Tuesday.
Muguruza, runner-up at the recent Australian Open, triumphed 6-2 7-6 (8-6) in one hour and 37 minutes on Monday.
Playing her first match since losing to Laura Robson in the second round of the US Open in August 2012, the Belgian was rusty at times as she racked up 10 double faults and gave up 15 break points.
However, Clijsters' fight and impressive groundstrokes in the second set would have given her plenty of hope for the months ahead.
Clijsters' opponent changed when Kiki Bertens withdrew from the event after winning in St Petersburg, but in-form Muguruza represented a similarly daunting first task in her comeback contest.
The 36-year-old was broken in a 10-point opening game and dropped serve again later in the first set.
She forced her first break points as Muguruza served for the opener at 5-2 but could not convert three opportunities as the Spaniard held.
A slow start also impacted four-time major champion Clijsters in the second set, as Muguruza claimed an immediate break and then struck once more in her opponent's next service game to move 3-0 up.
Clijsters showed grit and broke Muguruza for the first time in game four and later superbly claimed a second break to level matters, eventually forcing a tie-break.
She won the first two points of the breaker only for her younger rival to go on a streak of four that included a superb cross-court forehand winner.
At 6-5 in front, Muguruza hit a forehand long on her opening match point but she ultimately sealed victory with her next opportunity thanks to an unreturned serve
Having seen Swiatek brush aside Coco Gauff in straight sets in the first match of the day, Krejcikova would have been confident of doing likewise after taking the opener against Pegula.
Third seed Pegula battled back to take the second set, though, and the American appeared to have momentum on her side, only to bow out in a one-sided decider, losing 6-1 5-7 6-0 for her first defeat to Krejcikova.
The pair's only prior meeting had been a straight-sets win for Pegula at the Australian Open earlier this year.
Pegula's sole other tournament since Melbourne had ended in similar circumstances to this one, with a 6-3 6-0 crushing at the hands of Swiatek in the final of last week's Qatar Open. The Pole is who Krejcikova must play next.
Krejcikova is the first player since Svetlana Kuznetsova in Cincinnati in 2019 to beat two top-three opponents at the same WTA 1000 tournament.
Yet after seeing off number two Aryna Sabalenka in the quarter-finals and number three Pegula in the semis, she faces the world number one in the final.
Swiatek has had a rather more straightforward path, granted a walkover in the last eight and then, on Friday, playing Gauff, who she continues to dominate.
The Pole is now 6-0 across her career against Gauff, winning all of those matches in straight sets.
Gauff at least made Swiatek work a little harder than she has in many recent matches, going down 6-4 6-2 – the first match since Melbourne in which the number one has not won a set either 6-0 or 6-1, piling up the 'bagels' and 'breadsticks'.
Swiatek is 2-1 against Krejcikova for her career, although the Czech won their most recent meeting and their only encounter in a final in Ostrava last year.
By following up victories over Aryna Sabalenka and Jessica Pegula with a ruthless 6-4 6-2 dismantling of Swiatek, Krejcikova became just the fifth woman to beat each of the world's top three players at a single tournament in the last 40 years.
Krejcikova entered Saturday's meeting as the only player to have beaten Swiatek in her eight hard-court finals at tour level, having done so at the Ostrava Open last October.
The Czech looked to be drawing on that experience as she made a flying start, breaking in the opening game through a well-struck backhand.
Though Swiatek responded with a break of her own in the sixth game, a rare double fault from the Pole saw the momentum swing Krejcikova's way.
Another excellent backhand return gave Krejcikova the opening set's decisive break, after which a visibly frustrated Swiatek was handed a time violation by the umpire.
Things did not get much better from there for the three-time grand slam winner, with a series of masterful returns helping Krejcikova seal two dominant breaks before wrapping things up.
Having clinched a highly impressive win within 91 minutes, Krejcikova told Amazon Prime Video: "It means a lot.
"It was a great week for me, I was improving with every single game and today, I think I showed my best.
"I really have to admire Iga for what she is doing. To me, she is a big inspiration and she motivates me every day. It was a great final and I'm definitely happy with the result."
Djokovic had started 2023 by coming out on top in all 15 of his matches and winning the Australian Open, with his overall winning streak standing at 20 games.
But Medvedev ended the world number one's perfect start to the year with a superb display to take a 6-4 6-4 triumph on Friday.
The 27-year-old, who himself made it 13 consecutive wins, broke Djokovic twice on the way to taking the opening set.
Medvedev's high standard of play continued in the second, breaking Djokovic in the first game before holding in all five of his service games to secure a straight-sets victory.
"When you play against Novak you just have to play your best," Medvedev said after the win. "Kind of hope he doesn't play his best on the day because when he plays his best, well he has 22 grand slams, so even if you play your best, it is going to be tough, not sure you win.
"I managed to play a higher level than him today. In the second set I didn't face one break point, but there were so many 30-30 games. But I managed to stay composed and I am happy to be in the final tomorrow."
His win means he will face countryman Rublev in the final after the reigning champion kept his hopes of retaining the title alive with a 6-3 7-6 (11-9) success over Alexander Zverev.
Rublev had never previously won a match or set against Zverev in five previous meetings, but won three of the German's service games in the opener to go a set ahead.
The second seed was out-aced nine to two in the second set but managed to force a tie-break, going on to survive a set point before eventually securing the win on his sixth match point.
Rublev will look to join Roger Federer and Djokovic as only the third repeat champion at the tournament when he takes on Medvedev in Saturday's final.
The compatriots have met six times previously with Medvedev winning four of them, though Rublev has taken victory in their last two match-ups.
Former world number one Medvedev won 6-2 6-2 in an hour and eight minutes, adding to recent victories in Rotterdam and Doha as he extended his winning streak to 14 matches.
It gave him a tour-leading 19th match win of the season, edging ahead of Britain's Cameron Norrie, and means Medvedev will vault above Rublev to reach sixth in the new ATP rankings.
Appearing in his 30th tour-level final, Medvedev picked up his 18th career title and improved his head-to-head advantage to 5-2 against his compatriot.
He broke serve in the first and seventh games to sweep through the opening set, serving out to love to clinch it, and Rublev, who was the defending champion, offered no greater resistance in the second.
After beating Novak Djokovic in the semi-finals, this was supremely clinical from Medvedev, setting him up for tilts at the Masters 1000 events in Indian Wells and Miami over the coming weeks.
"It's amazing," said Medvedev in an on-court interview, "because the start of the year was not perfect."
He lost in round three of the Australian Open to Sebastian Korda, but has put that January jolt firmly behind him.
"In tennis, when you don't win tournaments, you are always doubting, no matter what happens in practice," Medvedev said. "So I was doubting a lot and now it just feels better. I was really happy with these three weeks and I'm looking forward to the next ones.
"Sometimes you feel you're doing all the right shots and you're losing matches, and sometimes you kind of don't even think, just go it, go for some crazy stuff. A lot of shots this tournament were landing which were maybe not supposed to be, and when confidence is going sometimes that helps a lot."
Medvedev's win makes him the third player in the last two years to land three titles in as many weeks, the ATP said, after Casper Ruud in July 2021 and Felix Auger-Aliassime.in October 2022.
Medvedev entered this week knowing victory at the Mexican Open would see him move to the top of the ATP rankings for the first time.
But the Russian was still waiting to play his quarter-final on Thursday when his ascension was confirmed courtesy of Djokovic's last-eight defeat in Dubai.
Djokovic, a seven-time year-end number one, had led the rankings for 86 consecutive weeks, boosting his record total to 361 weeks.
In his first tournament since missing the Australian Open, however, the five-time Dubai champion struggled to match 123rd-ranked Vesely and went down 6-4 7-6 (7-4).
Djokovic might have known what to expect, having lost his only prior meeting with Vesely in Monte Carlo in 2016.
The Serbian looked like getting to grips with his opponent at the start of the second set, applying pressure, but was then broken again and had to respond strongly to reach a tie-break.
Again, Vesely led, and Djokovic's match was summed up by a double-fault immediately after winning back the mini-break, allowing the Czech to prevail.
The victor hailed the end of Djokovic's reign, saying in his on-court interview: "It's great for tennis to have somebody new as world number one again.
"We all know Novak missed the Australian Open, but he's been such a champion, as world number one for 361 weeks.
"Tennis needs new number ones, new generations coming up, so I think it's just great."
As Vesely advances, second seed Andrey Rublev will fancy his chances of a second straight ATP Tour title after his win at the Open 13 Provence.
Rublev stretched his winning streak to seven matches in coming from behind to beat Mackenzie McDonald and make the semi-finals, where he will play Hubert Hurkacz, who defeated Jannik Sinner.
Daniil Medvedev had to contend with the powerful serving of Giovanni Mpetshi Perricard, before advancing to the quarter-finals in Dubai.
Daniil Medvedev was back in action for the first time since pulling out of the Qatar Open with food poisoning last week.
Mertens said she "just didn't want to let go" after coming back from the brink to end Jessica Pegula's fine run with a 5-7 7-5 6-0 victory.
The Belgian looked to be heading out when she faced a 5-2 deficit in the second set, yet saved three match points to force a decider.
"I kept on fighting and that was the spirit today," said world number 18 Mertens.
Former world number one Muguruza is Mertens' semi-final opponent, the Spaniard having come from a set down to beat third seed Aryna Sabalenka 3-6 6-3 6-2.
Muguruza lost out to Petra Kvitova in the final of the Qatar Open last week, but looks on top form as she closes in on another championship match.
Sabalenka fell foul of Muguruza in Doha, and the Belarusian was unable to gain revenge as the ninth seed earned a 16th win of the season.
There was to be no place in the last four for 16-year-old Gauff, who came up short against world number 54 Jil Teichmann.
Gauff, who defeated Teichmann twice in Australia in February, was broken to go 5-3 down in the first set and could not respond.
A second break in Teichmann's favour put Gauff on the back foot in the second, and the Swiss then saved three break points to nose into a 3-1 lead.
The contest was settled on Gauff's serve – Teichmann taking the match at the second time of asking to tee up a last-four clash with Barbora Krejcikova, who beat Anastasia Potapova 6-0 6-2 in a little over an hour.
Krejcikova was beaten in the doubles final last year, and has claimed her place in the singles semi-finals of a WTA 1000 event for the first time.
The in-form Spaniard required just one hour and nine minutes to win 6-0 6-4 against the number eight seed and reach the final eight for the fourth time in seven appearances at the tournament.
Reigning French Open champion Swiatek came into the contest on a six-match winning streak but her resistance seemed to falter after she dropped serve in the opening game and then failed to capitalise on two break points in the second.
Muguruza, whose 2021 record now stands at 15 wins and four defeats, was comparatively ruthless against an opponent who landed with just 38 per cent of her first serves.
The former world number one and double grand-slam champion let a 3-1 lead slip in the second set before resuming control through her punishing forehand, getting the job done on the first match point with an ace.
She will be back into action on Thursday against Aryna Sabalenka. The Belarusian, who beat Anett Kontaveit 6-3 6-2, lost in three sets to Muguruza at the Qatar Open last week.
"Back-to-back matches is good," said Muguruza. "That means I'm playing the top players, that means I'm getting into the deep rounds. I'm looking forward for another battle."
Coco Gauff reached the last eight of a WTA 1000 event for the first time after a straight-sets win over qualifier Tereza Martincova.
The American, who turns 17 on the day of the final, won 6-4 6-2 to set up a showdown with Jil Teichmann, a 6-3 6-3 winner over Ons Jabeur.
Second seed Karolina Pliskova was a surprise casualty, losing in less than an hour to Jessica Pegula. The world number 36, who also beat Pliskova in Qatar, will face Elise Mertens after she beat Caroline Garcia 6-4 6-2.
The last remaining former champion in the draw, Belinda Bencic, suffered disappointment on her 24th birthday as she lost 6-1 2-6 7-5 to wildcard Anastasia Potapova. She will take on Barbora Krejcikova, who eliminated Svetlana Kuznetsova.
The Spaniard saw six match points come and go in a battle lasting two hours and seven minutes before eventually closing out a 6-4 7-6 (7-5) win.
Having reached the final in Doha last week, where she lost to Petra Kvitova, Muguruza is the fifth player this century to reach back-to-back finals in the Middle East double, after Martina Hingis, Justine Henin, Caroline Wozniacki and Svetlana Kuznetsova.
The two-time major winner has now reached three finals in her past four tournaments and has won 17 matches in 2021.
Despite being ahead for much of the match, Muguruza was nonetheless pushed hard by Mertens, who fought back to beat Jessica Pegula in the quarter-finals after facing three match points.
She led by a set and 5-3 but Mertens continued to come up clutch at key points until Muguruza at last completed the job with a smash in the tie-break.
"You have to be all the time concentrated, otherwise she will come back," she said. "I didn't lose the focus even though I couldn't close it [at first] – I was just looking forward to the next opportunity.
"I didn't think I played bad on the match points. They were just tough points that didn't come to my side. She was very good in defence and on those points, I felt she brought her magic. But I was like, 'Okay, I'm playing well, sooner or later I will convert the match point'. I didn't lose the concentration or get too irritated."
Muguruza will face Barbora Krejcikova in the final, the Czech defeating Jil Teichmann 7-5 6-2.
Krejcikova saved 10 of 11 break points as she reached just the second Tour final of her singles career and has yet to drop a set at this tournament.
The world number 63 is the lowest-ranked singles finalist in history in Dubai, with that previous record held by Virginie Razzano, who was ranked 58 in the world when she lost to Venus Williams in 2009.
A day of upsets left Ons Jabeur, the eighth seed, as the top remaining player in the draw.
Some big names helped deliver the shocks, though, with world number two Sabalenka usurped by two-time Wimbledon champion and 2013 Dubai winner Petra Kvitova in straight sets.
Muguruza did not look like being one of the scalps as her title defence continued against Veronika Kudermetova.
But after taking the first set, the reigning WTA Tour Finals champion went down 3-6 6-4 6-4.
French Open champion Krejcikova, beaten by Muguruza in the final last year, also exited the tournament at the hands of Dayana Yastremska 6-3 7-6 (7-3).
Iga Swiatek let a set lead slip to Jelena Ostapenko, while two-time Dubai champion Elina Svitolina collapsed to lucky loser Jil Teichmann 7-6 (7-0) 6-2.
Jabeur, a winner against Jessica Pegula, was the only seed to win in a ruthless round of 16.
However, her reward in a still stacked quarter-final draw is a meeting with Simona Halep, another who has twice won in Dubai.
The former French Open and Wimbledon champion has produced some of the best tennis on tour this year but had gone without a trophy to back that up.
However, she put that right with a 7-6 (8-6) 6-3 victory over surprise finalist Krejcikova, a doubles specialist who has never ranked inside the top 50 in singles.
Coach Conchita Martinez has been absent from Muguruza's recent matches after testing positive for COVID-19, keeping tabs with mobile phone footage from courtside.
"She got the virus and was so upset she couldn't come, so this one is for her," Muguruza said.
Muguruza's most recent title had come at the 2019 Monterrey Open, where she successfully defended her title.
She was runner-up at the Australian Open in 2020 and in the early stages of this season made it through to finals at the Yarra Valley Classic and the Qatar Open.
She was beaten by Ash Barty in the first of those, in February, and by Petra Kvitova in Doha last weekend, but Muguruza made sure she did not spurn her latest chance to lift a trophy.
Krejcikova had bizarrely taken a medical break before the match began, seeking treatment on a thumb injury, but that did not prevent her being competitive.
The gruelling first set contained two breaks of serve for each player, and the second was also tightly contested before Muguruza took the title on her second championship point when her opponent went long with a forehand.
Muguruza said on Amazon Prime: "It's a great achievement. I've been coming here for many years and felt I was close but not enough.
"Finally today I got the champion's trophy and I'm very happy after losing a few finals in a row to get this one.
"I feel the consistency is hard to get, but being able to play three finals is a great sign that we are on the right way."
Murray and Djokovic both progressed through the first round at the Dubai Tennis Championships on Monday.
The Serbian's 6-3 6-3 win over Lorenzo Musetti marked his first on the ATP Tour in 2022, coming in the wake of his deportation from Australia due to his vaccination status ahead of the first major of the calendar year.
It remains unclear if Djokovic will be permitted to compete at this year's other majors - the French Open, Wimbledon and the US Open - given he remains unvaccinated.
"Like I said at the time, I don't agree with his decision. I think it would be a lot easier for him, obviously, if he was to get vaccinated," Murray told reporters after beating Australian Christopher O'Connell 6-7 (4-7) 6-3 7-5 in Dubai.
"But I also didn't like seeing him in the situation that he was in Australia as someone that I respect and have known since I was a child. I didn't like seeing that.
"There is consequences to the decisions he's made just now. He obviously has to accept that. But I don't think it's great for tennis if our best player is not competing in the major events."
Djokovic admitted after his win over Musetti that, as it stands, he cannot enter the United States to compete at next month's prestigious Indian Wells Masters, let alone the US Open.
The world number one added that he was hopeful the situation may change "in the next few weeks".
Murray reached the final of the Qatar Open, which he lost 6-4 6-4 to Daniil Medvedev on Saturday, and had to play three sets in every match during his run to the showpiece.
The world number 52 impressed in Doha, including beating Alexander Zverev and saving five match points against Jiri Lehecka in his semi-final.
However, the toll on the 35-year-old seems to have led to his decision not to participate in Dubai, with the tournament beginning on Monday.
A statement from the tournament read: "We regret to inform you that Andy Murray is unable to participate in this year's tournament.
"Andy has been dealing with a recurring hip injury that has unfortunately forced him out of Dubai. We wish Andy a speedy recovery and hope to see him back on the court in Dubai soon."
Murray's win over Lehecka in Qatar meant he moved level with Jimmy Connors in fifth on the list for most ATP hard-court wins in the Open Era (489).
Victorious in 2006, Nadal has not played at the event since 2008 but will make his return when the competition begins on February 27.
Ranked second in the world, Nadal's campaign in the United Arab Emirates will take place after the first grand slam of the year in Melbourne, where he is bidding to retain the Australian Open title he won 12 months ago.
Since he last featured at the Dubai Tennis Championships, Nadal has established himself as one of the sport's greatest players, something Colm McLoughlin, executive vice chairman and chief executive of the tournament's sponsor Dubai Duty Free, was keen to highlight.
"As one of the most instantly recognisable personalities in global sport, and one of the most decorated players to ever grace the game, we are absolutely thrilled to welcome Rafa back to the Dubai Tennis Championships after 15 years," he said.
"The last time Rafa played in Dubai, he had won three grand slams. He returns having amassed more grand slam titles than any other male player in history."
The 36-year-old followed last year's triumph in Australia with victory in the French Open for a record 22nd grand slam title.
Andrey Rublev won last year's Dubai Tennis Championships title, beating Jiri Vesely 6-3 6-4 in the final.
The world number two has been struggling with a lower back injury sustained prior to the Australian Open, which he exited in the quarter-finals at the hands of Stefanos Tsitsipas.
Nadal has not competed since, having subsequently pulled out of the ATP Cup and Rotterdam Open after being advised to give his back time to heal.
And the 20-time grand slam winner will delay his return for a little while longer after deciding to skip the upcoming ATP 500 event in Dubai.
"I would like to thank the @DDFTennis for the wild card invitation sent to me," Nadal posted on his Twitter page on Thursday.
"We seriously thought about coming to play, but I don't think I am ready to play yet. Once again thanks to the tournament's kind invitation and best of luck with the tournament."
The Spaniard added in a later tweet: "And special thanks to Tournament Director Salah Talak since I am aware of his efforts to ensure a smooth arrival to play Dubai during this unprecedented Coronavirus pandemic and difficult times for all."
Nadal won his only Dubai Tennis Championships title in 2006 with victory over Roger Federer – the competition's record eight-time winner – in the final.
Federer is scheduled to take part in this year's tournament after making his long-awaiting return from a 14-month injury lay-off at the Qatar Open this week.
Medvedev's 6-2 6-3 victory over Japan's Yoshihito Nishioka saw him advance to the final four of the Mexican Open in Acapulco on Thursday, where he will face Rafael Nadal in a repeat of last month's Australian Open final classic.
The Russian advanced shortly after Novak Djokovic's shock loss to Jiri Vesely at the Dubai Tennis Championships, which ensured that he will start next week atop the ATP world rankings for the first time.
The news came shortly after Russian president Vladimir Putin launched a military assault on neighbouring Ukraine, an act that has attracted condemnation from across the sporting world.
"Watching the news from home, waking up here in Mexico, was not easy," Medvedev told reporters.
"By being a tennis player, I want to promote peace all over the world. We play in so many different countries. I've been in so many countries as a junior and as a pro.
"It's just not easy to hear all this news. I'm all for peace. In these moments, you understand that tennis sometimes is not that important.
"It was not easy to play and I'm happy that I managed to win the match, but it was a bit of a rollercoaster day for me."
Medvedev's compatriot Andrey Rublev had earlier spoken out in favour of peace, calling the situation "terrible" in an Instagram post.
"In these moments you realise that my match is not important," Rublev's post read. "It's not about my match, how it affects me. What's happening is much more terrible.
"You realise how important it is to have peace in the world and to respect each other no matter what, to be united.
"We should take care of our Earth and of each other. This is the most important thing."
Rublev teamed up with Ukrainian Denys Molchanov to win the Open 13 Provence doubles title in Marseille just days ago, having also won the singles title at the tournament in southern France.
Rublev beat Hubert Hurkacz 3-6 7-5 7-6 (7-5) on Friday to progress to the final of the Dubai Tennis Championships.
After confirming his place in a showdown with either Denis Shapovalov or Jiri Vesely, the 24-year-old world number seven took a pen and scribed "no to war" on the lens of a television camera.
It is not uncommon for players to write messages on camera lenses, but a plea for peace was an emotive move from Rublev.
On Thursday, Russia invaded neighbouring Ukraine following weeks of rising political tensions. The conflict escalated further still on Friday, with reports of fighting within the capital city of Kyiv.
Rublev's actions came after Medvedev – who will succeed Novak Djokovic as world number one next week – said he wanted to "promote peace".
Medvedev has reached the final four of the Mexican Open in Acapulco.
Rublev had previously expressed his wish for peace in a news conference at the Dubai event.
"In these moments you realise that my match is not important," Rublev said, with a video clip shared to his official Instagram account.
"It's not about my match, how it affects me. What's happening is much more terrible.
"You realise how important it is to have peace in the world and to respect each other no matter what, to be united.
"We should take care of our Earth and of each other. This is the most important thing."
