Novak Djokovic came through a bruising battle with seventh seed Andrey Rublev to maintain his bid for a record-equalling eighth Wimbledon men's title.
The Serb, also aiming to match Margaret Court's record of 24 major singles titles, fought back to win 4-6 6-1 6-4 6-3 in the quarter-finals.
Djokovic, 36, will play Italy's Jannik Sinner in the last four on Friday.
Sinner, 21, reached his first Grand Slam semi-final by beating Russian Roman Safiullin 6-4 3-6 6-2 6-2.
In contrast, second seed Djokovic will be contesting a 46th major semi-final - equalling Roger Federer's all-time men's record.
It is a repeat of their quarter-final last year when Sinner came close to beating Djokovic, before the veteran fought back from two sets down to win.
Four-time defending champion Djokovic's hard-fought win against Russia's Rublev was his 33rd consecutive victory at the All England Club.
He has not lost a completed match in SW19 since 2016 and has not been beaten on Centre Court since losing the 2013 final against Britain's Andy Murray.
"They are just numbers. In a tournament, I don't like to spend too much time thinking about statistics," said Djokovic.
"It is an active tournament, I'm still in it and all I'm thinking about is my next match.
"It is only going to get tougher, but I like the way I played."
Djokovic 'loving' still being the man to beat
While Djokovic knows exactly what it takes to reach the semi-finals of a major, Rublev had never experienced the feeling of winning a Grand Slam quarter-final.
Rublev had lost all seven of his previous major quarter-finals - including a defeat by Djokovic at this year's Australian Open where he only won seven games.
A light-hearted comment he made before the meeting in Melbourne, saying he wished Djokovic had been in the other side of the draw, was afterwards construed as being indicative of the lack of belief he showed on court.
This time, Rublev started full of confidence. However, the 25-year-old could not sustain it as his opponent showed how he relishes putting younger players in their place.
Asked about needing to respond to being the man to beat, Djokovic said: "I love it. It's true. Any tennis player wants to be in the position where everyone wants to beat you."
The pair traded big blows from the baseline and, after saving three break points to hold for 3-3, Rublev pinched Djokovic's serve for 5-4 before serving out the opener.
It was the first time Djokovic had trailed in a match at this year's Championships.
Like the Wimbledon crowds have seen so often over the years, he responded by finding an even better level.
Serving more accurately and upping his return percentage helped the Serb win more of the shorter rallies, allowing him to break for 2-0 and again for 4-0 as he quickly took the second set away from Rublev.
Rublev regained his level in the third yet still fell a break down at 3-2. But he continued to press and applied severe pressure when Djokovic tried to serve out the set.
A monumental game saw Djokovic save three break points and, after reacting to the crowd getting behind Rublev by demanding more noise when he saved them, the man from Belgrade still found a way to take his fifth set point.
Rublev somehow had to find another level. Djokovic refused to let him.
Another early break put Djokovic in command and he sealed his place in a 12th Wimbledon semi-final by taking Rublev's serve again.
Sacrifices pay off for Sinner
Sinner had lost his four previous major quarter-finals but dominated against Safiullin after a wobble in the second set to earn his breakthrough win.
He becomes the youngest man to reach the Wimbledon men's singles semi-finals since 2007, although that will be beaten by Carlos Alcaraz or Holger Rune, who contest their quarter-final on Wednesday.
"It means a lot to me," Sinner said, after standing arms aloft as he sealed the win.
"We put in a lot of work in many, many hours - a lot of sacrifices. It is a very nice moment for me."
After clinching the first set with a single break of serve, Sinner, a former top junior skier, led 3-1 in the second before losing five games in a row as Safiullin levelled.
The 25-year-old Russian, who sits 92nd in the world and was bidding to be the lowest-ranked player to reach the men's last four since 2008, was unable to make the final two sets a contest once Sinner regained his composure.
"I was break up in the second and got down a little bit," Sinner said. "I am very happy with how I reacted."
