There were victories for John Isner and Dan Evans as the Madrid Open got up and running on Sunday.

Big-serving American Isner overcame Filip Krajinovic 7-6 (10-8) 6-4 and will face either Cameron Norrie or Kwon Soon-woo in the round of 32.

Isner is joined in the next round by Evans, who eased past Federico Delbonis 6-3 6-4 to set up a last-32 meeting with either Roberto Bautista Agut or Jenson Brooksby.

Fellow Briton Jack Draper also enjoyed a straight-sets victory, edging out Lorenzo Sonego 6-4 6-3 to book a clash with number six seed Andrey Rublev, who received a bye.

Monday's action will see wildcard Andy Murray face Dominic Thiem and 10th seed Jannik Sinner take on Tommy Paul.

Sebastian Baez sealed a straight-sets win against Frances Tiafoe in the final of the Estoril Open on Sunday.

The Argentinian put in a powerful performance to ease past the American fifth seed, winning 6-3 6-2 in Portugal in just 74 minutes.

It was a fast start from Tiafoe, breaking Baez in the opening game, before the 21-year-old secured back-to-back breaks of his own in the fourth and sixth games to edge ahead, ultimately taking the first set.

The second set started evenly, but from 2-2, Baez put his foot down, again breaking consecutive Tiafoe service games, before serving out for the title.

The first serve was the difference for Baez, making 64 per cent of his compared to Tiafoe, who managed just 39 per cent.

Baez was also more effective when he needed his second serve, winning 61 per cent of points, with his opponent winning only 39 per cent from his own second serve.

Holger Rune won his first ever ATP tour title on Sunday, but admitted it was the "worst way to win a final" after opponent Botic van de Zandschulp retired in the BMW Open final.

Both men were playing in their maiden tour-level final on debut at the ATP 250 event in Munich, and Rune becomes the third-youngest Munich champion in the Open Era.

Eighth-seed Van de Zandschulp was leading 4-3 in the first set, with his Danish opponent serving at 40-15 when the Dutchman retired due to an aching chest.

"This was probably the worst way to win a final,” Rune said. "I was obviously expecting a very tough match and he came out very strong.

"I just wish him all the best, a speedy recovery, and we all just hope to see him back on the court very soon."

Rune, who turned 19 on Friday, had a memorable week in Germany, including securing his first victory against a top 10 opponent when he beat world number three Alexander Zverev in the second round, before also getting past Jiri Lehecka, Emil Ruusuvuori and Oscar Otte on his way to the final.

"I'm super happy, of course," Rune continued. "As I said, not the way I want it to end, but if I look through the week, what a week.

"I played some unbelievable tennis, really fighting my way through it. To be playing here in Munich and winning my first ATP title in front of such a brilliant crowd, I couldn't really ask for more."

Rafael Nadal remains confident that he will be fully fit in time for this month's French Open, despite still suffering from a "very disabling" rib injury.

The 35-year-old has been sidelined since sustaining a cracked rib during the Indian Wells Masters in March.

However, Nadal confirmed last week he intends to make his return to action on home soil at the Madrid Open next week.

And the Spaniard, who won a record 21st grand slam at the Australian Open in January, expects to be ready for Roland-Garros later this month.

"I have three weeks," he said on Saturday. "I trust that the daily training will help me to get ready.

"Here the demand [in high altitude in Madrid] is maximum, but what can be done is going to be done.

"The most important thing is to be healthy, but I think that going to Paris I'm on time. Three weeks is enough time to get competitive."

He added: "I have trained very little, because the rib is very disabling and also very painful. I had two very bad weeks and afterwards it has been very, very disabling.

"I haven't been able to do practically anything, but it's here, at home, in Madrid."

Thirteen-time French Open winner Nadal will face either Alexander Bublik or Miomir Kecmanovic in the second round of the Madrid Open.

The third seed is on a collision course with highly rated compatriot Carlos Alcaraz in the quarter-finals at the Caja Magica.

Frances Tiafoe downed fellow American Sebastian Korda in a hard-fought encounter to reach the final of the Estoril Open, while Holger Rune reached a first title match at the BMW Open.

Korda had eliminated top seed Felix Auger-Aliassime in the quarter-finals in Portugal to set up an all-American last-four clash, and looked on course to reach the final after winning the first set against Tiafoe.

However, the fifth seed roared back to seal a 4-6 7-6 (7-2) 6-4 victory and set up a final encounter with Argentina's Sebastian Baez, who beat Albert Ramos-Vinolas to reach his second tour-level final.

Baez also needed three sets in his semi-final clash after losing a competitive second-set tie-break, but he then produced a scintillating performance to win the decider without dropping a game, winning 6-3 6-7 (7-9) 6-0.

Elsewhere, Danish 19-year-old Rune sealed his first ATP tour final appearance by beating home favourite Oscar Otte 6-4 6-4 at the BMW Open in Munich.

Rune, who has enjoyed a dream week in Bavaria after sensationally downing Alexander Zverev in the last-16 and failing to drop a single set in the tournament, revealed his ambitions to become world number one in the future after the victory.

"It's a pretty unreal feeling," he said of his semi-final win. "I didn't expect this at all coming into this tournament, and I just took it match by match. Obviously, I had a tough draw, playing Zverev in the second round, but I knew it was going to be tough, so I was ready from the beginning, and I'm super happy to be in the final.

"It's getting better and better, I'm improving every day, and this is what matters. I have some goals to be number one in the world, and you have to start somewhere."

Rune will face eighth seed Botic van de Zandschulp in the final after the Dutchman rallied to beat Miomir Kecmanovic 2-6 7-6 (7-4) 6-4 in his own final-four encounter. 

Carlos Alcaraz has learned never to give up after facing Rafael Nadal, with the pair on a collision course to meet again in next week's Madrid Open quarter-finals.

Alcaraz has enjoyed a hugely impressive season to date, having last week added the Barcelona Open to the titles won in Rio de Janeiro and Miami already in 2022.

Following on from that triumph in Catalonia, Alcaraz – who turns 19 next week – became the youngest male player to break into the top 10 since Nadal 17 years ago.

He boasts a record of 23-3 this year, one of those defeats coming at the hands of Spanish great Nadal in the semi-finals of Indian Wells in March.

That encounter lasted over three hours, with Nadal digging deep in California to prevail 6-4 4-6 6-3, only to lose in the final to Taylor Fritz.

Nadal was clearly troubled by injury during his defeat to Fritz and has subsequently taken a break to recover from a rib problem.

The pair are set to collide once again in Madrid next week should they both come through their second and third-round matches.

Speaking ahead of the draw being made on Friday, Alcaraz revealed he has taken inspiration from facing Nadal, who won a record 21st Grand Slam at the 2022 Australian open.

"I learned about the fighting spirit, of never giving up," the teenager told Spanish talk show El Hormiguero.

"Many people will have also seen the Australian Open match, he was losing and came back almost miraculously.

"From that match against him [at Indian Wells] I get the fighting spirit, never give up and fight until the last ball."

Top seed Novak Djokovic is also in Alcaraz and Nadal's side of the Madrid Open draw, while Andy Murray and Dominic Thiem will meet in the pick of the first-round clashes.

Top seed Felix Auger-Aliassime fell to Sebastian Korda in the Estoril Open quarter-finals, while Casper Ruud was sent packing at the BMW Open. 

Auger-Aliassime won just 50 per cent of points behind his first serve as Korda claimed an impressive 6-2 6-2 success over the Canadian in one hour and 29 minutes. 

In the semi-finals Korda will take on fellow American Frances Tiafoe, who edged out Alejandro Davidovich Fokina 7-6 (7-5) 5-7 7-5 in a tight encounter. 

The other last-four clash will see Albert Ramos Vinolas take on Sebastian Baez. 

Ramos Vinolas bested Fernando Verdasco 6-2 6-2 to set up his meeting with Baez after the Argentine rallied from a set down to defeat Richard Gasquet 3-6 6-1 6-4. 

At the BMW Open, second seed Ruud fell to Botic van de Zandschulp in the quarter-finals. 

The Dutchman won their only previous encounter en route to the last eight at last year's US Open and he triumphed 7-5 6-1 in Munich. 

"Maybe the score is easier than it really was," said Van de Zandschulp. "The first set [was] really tight, I think. A great battle in the first one. I had some opportunities to break him in the beginning and didn't take them. Gladly [at] five-all I made the break and held the serve at 6-5. 

"[The] second set was a little bit easier, but I think I played really well today." 

Next up for Van de Zandschulp is Miomir Kecmanovic, who defeated Nikoloz Basilashvili 7-6 (7-5) 6-2. Holger Rune will continue his impressive run against Oscar Otte in the other semi-final after they overcame Emil Ruusuvuori and Alejandro Tabilo respectively. 

Felix Auger-Aliassime survived an early scare to reach the Estoril Open quarter-finals with victory over Carlos Taberner on Thursday.

The top seed is targeting a second title of 2022, having already triumphed in Rotterdam earlier in the campaign.

However, his quest looked in doubt when Taberner dominated the opening set 6-1.

But the world number 10 responded in equally commanding fashion; controlling the next two sets to prevail a 1-6 6-2 6-2 victor.

Auger-Aliassime, who also overcame Taberner in Barcelona last week, will play Sebastian Korda in the last eight after the American beat Benjamin Bonzi 6-3 6-3.

Meanwhile, Santiago finalist Sebastian Baez is through to his third quarter-final of 2022. The world number 59 recovered from a set down to deny third seed Marin Cilic 1-6 6-1 6-4.

Richard Gasquet awaits after the 2015 champion beat Hugo Dellien 7-6 (7-5) 6-2.

Over in Munich, second seed Casper Ruud took a while to find his groove before overcoming Slovakia's Alex Molcan 3-6 6-4 6-4.

Following Alexander Zverev's exit on Wednesday, the Norwegian is the highest remaining seed and is targeting a second title of the season having triumphed in Buenos Aires two months ago.

Next up for him is Botic van de Zandschulp, who won 86 per cent of his points on first serve as he defeated Egor Gerasimov 6-2 6-3.

Meanwhile, Oscar Otte stunned third seed Reilly Opelka 7-6 (7-4) 6-2 to reach his second quarter-final in as many weeks, having also reached that stage in Belgrade.

The German will play Cordoba runner-up Alejandro Tabilo, who advanced following the retirement of opponent Hugo Gaston through injury. 

Alexander Zverev is out of the BMW Open after a shock straight-sets defeat to Holger Rune in the last 16 in Munich.

The world number three and top seed had no answer to an impressive performance from Rune, with the young Dane ultimately easing to a 6-3 6-2 victory on Wednesday.

Rune set the tempo early on, moving Zverev around the court with plenty of drop shots and heading into a 4-2 lead, before saving two break points on his way to clinching the first set.

An early break in the second then seemed to give the 18-year-old the confidence to see out his first career victory against a top 10 opponent.

"It was a difficult match from the beginning," said Rune on-court after the win. "He's in the top three in the world and has been playing some unbelievable tennis, especially in the past year winning so many big titles.

"I have a lot of respect for him, and I obviously didn't expect to win in two sets, and with a score like this. But it was a really hard match, we played a lot of rallies and I'm really happy about my performance today."

Rune will play Emil Ruusuvuori in the quarter-finals after the Finn beat Maxime Cressy 6-3 6-3.

Elsewhere, fourth seed Nikoloz Basilashvili came from behind to overcome Ilya Ivashka 3-6 6-2 6-4, and will face Miomir Kecmanovic in the last eight after the seventh seed beat Daniel Altmaier 6-2 6-4.

There were also three round of 32 matches on Wednesday, with eighth seed Botic van de Zandschulp, Egor Gerasimov and Alejandro Tabilo all through to the last 16 in Munich.

Over at the Estoril Open, Alejandro Davidovich Fokina will play Frances Tiafoe in the quarter-finals after both advanced in Portugal.

Fourth seed Davidovich Fokina beat fellow Spaniard Bernabe Zapata Miralles 6-3 7-6 (7-5) while fifth seed Tiafoe got the better of Nuno Borges 7-6 (7-4) 4-6 6-0.

Fernando Verdasco is also through after a 6-2 6-3 win against Pablo Cuevas, and he will play fellow Spaniard and sixth seed Albert Ramos-Vinolas, who came from a set down against Kwon Soon-woo, 5-7 6-1 6-2.

Naomi Osaka believes teen tennis star Carlos Alcaraz has rejuvenated excitement around the ATP Tour, while she labelled Rafael Nadal as an inspiration ahead of the Madrid Open.

Alcaraz needed just 67 minutes to defeat Spanish compatriot Pablo Carreno-Busta 6-3 6-2 at the Barcelona Open last Sunday, claiming his third title of the season after wins in Rio de Janeiro and Miami.

The 18-year-old has surged to a career-high ninth in the world rankings, Alcaraz becoming the youngest player to crack the top 10 since fellow Spaniard Nadal achieved that feat at the same age in 2005.

Coincidentally, Nadal also broke into the top 10 after success on the same day (April 25) at the Barcelona Open and the pair will next compete in Madrid in the ATP 1000 Masters event, which starts on Sunday.

Former women's world number one Osaka revealed she is keen to cast an eye over the duo in the Spanish capital, where she faces a qualifier in the first round, as she hailed the impact Alcaraz has had.

"I feel like he's genuinely made everyone excited about the ATP and I haven't seen that in a very long time," Madrid Open wildcard Osaka said of Alcaraz, who boasts an impressive 23-3 record in the 2022 season.

"I'm not even really thinking about his age, like every time someone brings up his age, I'm like, 'Oh wow, I forget, that's so cool'.

"I think just his game style, just how pumped he is, how I feel like I'm watching him learn with every tournament.

"I don't know what his ranking was last year here, but I've watched almost every tournament that he's played, the US Open when he played [Stefanos] Tsitsipas and just to see the growth I think is really exciting for everyone."

Osaka has won all four of her grand slam titles on hard courts, but the 24-year-old will now search for clay-court success in Madrid.

Japanese Osaka has spent time preparing in Majorca, where she has used 13-time French Open winner Nadal as an inspiration, given his expertise on clay courts.

"I think I stole one of the things that he did and I've been practising it recently," she said of Nadal, who holds the record for most men's grand slam titles with 21 major triumphs to his name.

"It'll either go really good or really bad. There's like no in between. But I think as I've been doing it, it's been going pretty well.

"Honestly I've been wanting to watch the really good clay-court players practice because I feel like I'm the type of person that learns really fast if I see it up close and honestly it's a bit of a waste to have all these really good professional tennis players and not watch them."

Osaka suffered a second-round exit at the Indian Wells Masters in March, impacted by abuse from a heckler in the crowd, but rebounded by making the final in Miami, where she lost to world number one Iga Swiatek.

However, Osaka is looking to use the experience at Indian Wells, where she was reduced to tears by a spectator reportedly shouting "Naomi, you suck", as a learning curve to develop.

"I feel like there are a lot of moments in my career that are like extremely sad for me at the time but I kind of later look back on it and I think to myself, 'Well that really made me grow as a person, and even though I really hated the experience, I'm glad it happened to me'," she added.

"For me, that's one of those moments. I wish it didn't happen, but also I'm glad that it did.

"I feel like it prepared me for a lot of things that may or may not happen, but it's kind of like one of those things you have in your back pocket as experience."

Dominic Thiem's wait for the first win of his comeback goes on after he lost to Benjamin Bonzi at the Estoril Open.

Thiem was competing in just his second tour-level event of 2022 after suffering a wrist tear last June, having lost to John Millman at the Serbia Open last week. 

The 2020 US Open champion could not find a way through against Bonzi, who did not face a break point in prevailing 6-3 7-6 (11-9).

Bonzi will next face Sebastian Korda, the eighth seed a straight-sets winner over Pierre-Hugues Herbert.

Fifth seed Frances Tiafoe and sixth seed Albert Ramos-Vinolas defeated Dusan Lajovic and Jordan Thompson respectively, but seventh seed Tommy Paul lost to veteran Richard Gasquet.

At the BMW Open in Munich, sixth seed Dan Evans lost in his first match for the fourth time in five tournaments.

The sixth seed was beaten 6-4 6-4 by Maxime Cressy, while there were wins for Hugo Gaston, Ilya Ivashka and Oscar Otte.

Rafael Nadal plans to make his return from injury in his homeland at the Madrid Open next week.

Nadal has been sidelined since suffering a cracked rib during the Indian Wells Masters last month.

The 21-time grand slam champion on Tuesday revealed he has decided to make his ATP Tour comeback at the Caja Magica.

He posted on social media: "Despite preparation being difficult, I really want to play at home since the opportunities are few.

"[I want] To try to do it in the best possible way. See you in Madrid."

Taylor Fritz consigned Nadal, a five-time champion at the Madrid Open, to his first defeat of the year in the final at Indian Wells.

The Australian Open champion was visibly struggling to breath during that match after sustaining the injury during a semi-final victory over fellow Spaniard and heir apparent Carlos Alcaraz. The 35-year-old's 2022 record so far stands at 20-1.

Nadal's return is set to make his comeback just three weeks before he will be hoping to start his bid to win a 14th French Open title at Roland Garros.

Roger Federer will make his comeback at the Laver Cup in September before playing the Swiss Indoors Basel event in his home city.

It means the legendary 20-time grand slam winner is set to miss all four majors this year.

The eight-time Wimbledon champion will turn 41 in August, and it remains to be seen whether the two events turn out to be farewell tournaments before he retires.

Federer has battled knee trouble over the past two years and has barely featured on the ATP Tour, with his most recent appearance coming at Wimbledon last year, where he was beaten in the quarter-finals by Hubert Hurkacz, a straight-sets defeat that culminated in a 6-0 third set.

The Swiss great has undergone surgery in an effort to finish his career on his own terms.

News of his comeback plans were announced by the Swiss Indoors organisers, who issued a statement that said: "Ten-time singles champion and hometown hero Roger Federer has announced his comeback to the stadium at St Jakobshalle. The Swiss all-time great has confirmed his initial agenda will include the Laver Cup in London followed by the Swiss Indoors in Basel."

Responding to the announcement, Federer posted on Instagram: "Looking forward to playing back home."

The Laver Cup takes place in London from September 23 to 25, and the Swiss Indoors Basel runs from October 24 to 30.

Federer will play his opening match at the latter on Tuesday, October 25, the organisers said.

"The worldwide interest in the return of the hometown hero and 20-time grand slam champion to the ATP Tour is expected to be tremendous," the Swiss Indoors statement added.

Federer for a long time held the record for the most grand slam singles titles won by a man; however, he has been joined on 20 by Novak Djokovic, and Rafael Nadal moved out on his own with 21 by triumphing at the Australian Open this year.

Novak Djokovic will be able to defend his Wimbledon title this year as players will not need to be vaccinated against coronavirus to feature in the tournament.

World number one Djokovic was unable to compete in the 2022 Australian Open after he was deported from the country in January.

The Australian government cancelled the Serbian's visa on "health and good order" grounds and he failed with an attempt to overturn that decision in court.

Djokovic will be able to play in the grass-court grand slam at the All England Club, though, due to a lack of COVID-19 restrictions in the United Kingdom.

All England Lawn Tennis Club (AELTC) chief executive Sally Bolton said during a media briefing on Tuesday: "As you will be aware, the requirements set up by the government to enter the UK do not include mandatory vaccinations.

"Therefore, whilst of course it is encouraged, it will not be a condition of entry in order to compete in the Championships this year."

Djokovic can also play in the French Open following the easing of restrictions.

There will be no Russian or Belarusian players when Wimbledon is staged from June 27 to July 10 at SW19 due to Russia's invasion of Ukraine.

All England Club chairman Ian Hewitt says the decision to ban Russian and Belarusian athletes from Wimbledon was the "most responsible decision possible in the circumstances."

Organisers of the grass-court grand slam confirmed this month that players from both nations would be barred from featuring in the tournament due to Russia’s invasion of Ukraine.

The decision was met by a significant backlash, with world number eight Andrey Rublev describing the decision as "discrimination" and Novak Djokovic stating he could not support it.

But speaking at the 2022 Wimbledon media briefing, Hewitt sought to clarify the process by which the decision was made.

"After lengthy and careful consideration we came to two firm conclusions that have formed the basis for our decision," he told reporters.

"First, even if we were to accept entries from Russia and Belarusian players with written declarations we would risk their success or participation at Wimbledon being used to benefit the propaganda machine of the Russian regime which we could not accept.

"Second, we have a duty to ensure that no actions we take should put the safety of players or their families at risk."

All England Lawn Tennis Club (AELTC) chief executive Sally Bolton shed further light on the process of making such an "an immensely difficult decision." 

"We recognise that whatever decision we took would be setting a precedent," she added.

"We made our judgement in the scale of the response to an international war, the consequences of which reach far wider than the sport of tennis.

"We appreciate that this is an immensely difficult decision, and that people have different views which we respect and understand.

"We are deeply regretful of the impact that this will have on every single player who is affected.

"We are in ongoing dialogue with the players, with the tours, with the ITF and with our fellow grand slams, and will continue to work with them over the coming weeks.

"We believe that this decision is the only viable option for Wimbledon."

Wimbledon also confirmed that players who have not received a coronavirus vaccination will be allowed to enter the tournament. 

Djokovic hit the headlines when he was unable to play in the Australian Open this year after being deported due to his vaccination status.