|2019 Nitto ATP Finals|
|Venue: O2 Arena, London Dates: 10-17 November|
|Coverage: Watch live coverage of one match per day on BBC TV, BBC iPlayer and online; Listen on BBC Radio 5 Live Sports Extra; Live text on selected matches on the BBC Sport website and app. Click here for Live Guide.|
Rafael Nadal missed out on a place in the ATP Finals last four as defending champion Alexander Zverev claimed the remaining semi-final spot in London.
Nadal, who beat Stefanos Tsitsipas 6-7 (4-7) 6-4 7-5 in the afternoon session, needed Daniil Medvedev to beat Zverev to secure a place in the last four.
However, Zverev came through 6-4 7-6 (7-4) to eliminate Nadal and set up a meeting with Dominic Thiem.
Tsitsipas will face Roger Federer in the other semi-final on Saturday.
Swiss Federer, who is bidding for a seventh title at the tournament, plays Greek Tsitsipas from 14:00 GMT in a match which is live on BBC Two.
Germany's Zverev takes on Austrian Thiem from 20:00.
World number one Nadal had knocked Russian fourth seed Medvedev out of the tournament with his hard-fought victory over Tsitsipas.
Ultimately, it was a lifeless performance in his opener against defending champion Zverev on Monday that cost Nadal.
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Seventh seed Zverev has had a mixed season but put in a convincing performance against Medvedev to advance to the semi-finals.
The German broke Medvedev in the opening game of the match and capitalised as the Russian's serve faltered in the closing stages.
After staving off a break point, Medvedev held his nerve to force a tie-break, but a double fault allowed Zverev to serve out the match.
Zverev, who did not face a break point all match, fell to his knees after the final point, and said afterwards he could "still improve" on his performance.
"This arena is where I play my best tennis, we don't play in this atmosphere anywhere else in the world," he said.
"I think I've played two great matches. Only the best four players left are in the semis."
Close but not enough for Nadal
Nadal showed the grit, determination and never-say-die attitude that have been the hallmarks of his illustrious career to beat Tsitsipas in two hours and 52 minutes at the O2 Arena.
He was edged out of a tight first set in the tie-break before starting to hit more winners than unforced errors and tip the balance of the match in his favour.
Greek sixth seed Tsitsipas was the player under all the pressure on serve, facing nine break points in the match with Nadal needing to convert just one in each of the final two sets.
Nadal himself served supremely and did not face a single break point, but the 19-time Grand Slam champion has yet to win the season-ending tournament.
"I did all the things I could do, fighting until the end," Nadal told the crowd.
Tsitsipas, 21, was already assured of reaching the last four on his ATP Finals debut whatever happened against Nadal and, despite a lengthy battle against the top seed, says he still has "left something in the tank" for the weekend.
"During the match I thought about it a couple of times, but at the end I really wanted to win, and that win means a lot to me because it's against a tough player, the current world number one," said Tsitsipas, who won the ATP Next Gen finals last year.
"I didn't really go full, full. I could have gone even more full than that but I'm not disappointed by that.
"I wanted to win but probably wasn't willing to die on the court for that."
'I never thought at 33 I'd have this trophy' - Nadal finishes 2019 as number one
No matter what happened against Tsitsipas, Nadal was already assured of finishing the year as men's world number one.
The French Open and US Open champion clinched that accolade for the fifth time after nearest rival Novak Djokovic lost to Federer on Thursday, eliminating the Serb from the ATP Finals and therefore meaning he could not overtake Nadal to land the prestigious prize.
As well as the two Grand Slam wins, Nadal also won ATP Masters 1000 titles in Rome and Montreal.
The 33-year-old Spaniard is the oldest player to finish as the year-end number one since the ATP rankings were introduced in 1973.
Following his victory over Tsitsipas, Nadal was presented with a trophy marking the achievement on court at the O2.
"It's a real honour to receive this trophy. Honestly, what can I say? I am super happy," Nadal said.
"After all the things I went through in my career in terms of injuries, I never thought at the age of 33 and a half I would have this trophy in my hands again.
"It's something really, really emotional for me, a lot of work."