Novak Djokovic labelled Carlos Alcaraz as "special" and praised the Spaniard for "breathing new life into the world of tennis".
Serbian Djokovic defeated Pole Hubert Hurkacz 6-3 6-4 to reach his seventh Madrid Open semi-final, where he will meet Alcaraz, who overcame Rafael Nadal 6-2 1-6 6-3 on Friday.
Victory made 19-year-old Alcaraz the first teenager to beat record 21-time grand slam winner Nadal on clay on the ATP Tour.
Alcaraz has won his last five matches against top-10 opponents and next faces world number one Djokovic for a place in the final in the Spanish capital.
Djokovic was quick to hail Alcaraz, who will play in his third ATP Masters 1000 semi-final on Saturday.
"There are many things that are special about him," Djokovic said in a news conference.
"In the last decades, we have had some incredible champions [as teenagers] like Michael Chang. But, nowadays, we're not used to seeing someone who is a teenager and already breaks into the top 10 and plays at such a high level.
"His growth, his improvement and his trajectory, especially in the last six months, have been incredible.
"He is a very nice guy off the court. I had the opportunity to train with him and spend a little time off the court with him here in Madrid, and I must say that on all fronts, he is great on and off the court."
Quoted by Spanish media, Djokovic said of Alcaraz: "I love watching him play, like many other players on tour. I praise his game without a doubt. It's fantastic for our sport, without a doubt.
"I think it's fantastic that we have a young player who is doing so well and who is breathing new life into the world of tennis."
Alcaraz expressed personal delight after defeating clay-court great and compatriot Nadal, battling back from an injury worry in the second set.
"It means a lot to me. All the hard work I put in every day has paid off," he said in the aftermath of his victory. "To beat Rafa, the best player in history on clay, it means a lot.
"The fall in the second set affected me a lot. When I lost the set I went to the bathroom and thought I would be able to come back to do my best and try everything.
"I wanted to fight until the last ball and that was the key."
Nadal cruises past teen Blanch to tee up De Minaur rematch in Madrid
Darwin Blanch presented little challenge for Rafael Nadal, who dropped just one game in a convincing 6-1 6-0 triumph at the Madrid Open.
Nadal is feeling his way back to fitness, but 16-year-old qualifier Blanch offered little resistance to the 22-time major champion on Thursday.
Making his farewell appearance at the Madrid Open, where he has won five titles, Nadal needed just 64 minutes to progress to round two.
"I think today I played against an opponent with a great future in front [of him], but today, still making mistakes," said Nadal.
"I just tried to be there, be solid all the time without taking a lot of risks. It worked well. I'm happy to be through and I wish him all the very best for the future."
Nadal's reward is a rematch with Alex de Minaur, who he lost to last week in Barcelona.
Data Debrief
This game saw the largest age gap (21 years, 117 days) between two opponents in the history of ATP Masters 1000 events.
Nadal has now registered 57 wins at the Madrid Open, which is 20 clear of any other player.
Osaka eliminated by Samsonova in Madrid
Naomi Osaka was knocked out of the Madrid Open by Liudmila Samsonova after an entertaining second-round battle on Thursday.
Having won her first match on clay for two years against Greet Minnen a day earlier, Osaka was able to force a final set against 15th seed Samsonova but ultimately fell to defeat.
Samsonova won a close encounter 6-2 4-6 7-5 to book a clash with American Madison Keys – who defeated Irina-Camelia Begu in straight sets – in the next round.
Osaka had beaten Samsonova at Indian Wells last month and came close to securing another victory as she recovered well from losing the opening set.
But the Japanese star was broken to fall 5-6 behind in the final set, and the Russian made no mistake in ruthlessly closing out the victory.
Data Debrief: Samsonova ends losing streak
This was a crucial win for Samsonova, who came into the match having lost four consecutive contests, including that Indian Wells defeat to Osaka on March 9.
Samsonova did apply plenty of pressure in the final set – forcing five break points compared to just one for Osaka – and was ultimately rewarded in the closing stages of a contest that lasted two hours and 22 minutes.
Azarenka makes history with 200th WTA 1000 win
Victoria Azarenka made light work of progressing into the round of 32 at the Madrid Open and she made history in the progress.
Azarenka, a two-time finalist in Madrid, despatched Tatjana Maria 6-3 6-1 on Thursday.
It brought up her 200th victory at WTA 1000 events, which makes her the first woman to hit that milestone since the format was introduced in 2009.
The former world number one needed just 81 minutes on court to get the job done, and will face Sara Sorribes Tormo in the next round.
Data Debrief
This was Azarenka's first meeting with Maria, and her service game was excellent, with the Belarusian winning 63.2 per cent of her first-serve points. She also saved five break points, having offered up seven, and converted six going the other way.
Azarenka, who has won 10 WTA 1000 events, is 14 clear of next-best Simona Halep (186) on the list of women with the most WTA 1000 match wins.
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