In case you missed it earlier, Nadal will play Daniil Medvedev in Saturday's semi-final.
Medvedev, who lost to Nadal in a humdinger of a US Open final in September 2019, is assured of his place as the Group Tokyo 1970 winner.
World number one Novak Djokovic and Alexander Zverev battle it out for the right to face Dominic Thiem - who beat Nadal to top Group London 2020 - in the other semi-final.
'Reaching the semi-finals is very important'
Nadal 6-4 4-6 6-2 Tsitsipas
Rafael Nadal on reaching the ATP Finals semi-finals: "I think I played quite well for such a long time. That game at 5-4 in the second set affected me a little bit, but then I was able to get the break early in the third, then he broke me and I broke again.
"I was winning serves quite comfortably until that moment, after that everything changed and I started to serve worse.
"But in general terms it was a positive match for me. To reach the semi-finals in the last tournament of the year is an important thing."
Post update
Nadal 6-4 4-6 6-2 Tsitsipas
As always, Rafa doesn't rush as the microphone waits. A change of shirt, a dig around for the facemask and the bull-emblazoned tracky top. Now he is ready...
Post update
Nadal 6-4 4-6 6-2 Tsitsipas
Not to be for Stefanos Tsitsipas, who was aiming to become the first man to defend the title since Novak Djokovic in 2015.
While the impressive win against Andrey Rublev gave him hope, it was not to be with Dominic Thiem and now Rafa Nadal in tip-top shape.
Game, set and match Nadal
Nadal 6-4 4-6 6-2 Tsitsipas
Keep that space in the trophy cabinet ready and waiting...
Rafa rolls on! Nadal moves into the semi-finals as he looks to bag the ATP Finals title for, quite staggeringly, the first time.
The Spaniard seals his spot in the last four with a precise winner down the line. The grin accompanying his sideward glance at his box tells you exactly how he is feeling. Vamos!
Match point to Nadal
*Nadal 6-4 4-6 5-2 Tsitsipas
Ooof! A thumping ace down the middle puts Nadal within touching distance of the match... only for Tsitsipas to force deuce when Nadal drifts a return wide.
On we go...
Post update
*Nadal 6-4 4-6 5-2 Tsitsipas
Superb craftsmanship from Nadal, constructing the point beautifully and putting away a volley for 15-30. From that delicate touch, he goes to some hammer blows in the next point and Tsitsipas goes long for 30-30.
Post update
*Nadal 6-4 4-6 5-2 Tsitsipas
Hang on... Tsitsipas is not heading to the cloakroom and grabbing his coat just yet. The Greek asks a question of Nadal at 0-30...
Nadal serves for the match
*Nadal 6-4 4-6 5-2 Tsitsipas
So then, here we are. After the rollercoaster ride at the start of this set, Rafael Nadal is coasting towards the platform.
The Spanish second seed serves for the match - and his spot in the semi-finals.
Nadal breaks
*Nadal 6-4 4-6 5-2 Tsitsipas
Not only is Nadal serving better, he is still returning sharply. That, combined with Tsitsipas losing his way, racks up two break points and he takes the second one when Tsitsipas sprays a wild one with more force than a jet-wash operative.
Nadal holds
Nadal 6-4 4-6 4-2 Tsitsipas*
Remember when Nadal was holding serve comfortably and quickly? Yes, that. The world number two moves a step closer to the magic number with a blink-and you'll-miss-it hold to love.
The tornado which swept through the O2 and demolished a number of serves seems to have passed. Nadal is emerging from the wreckage and rebuilding quickly.
Post update
*Nadal 6-4 4-6 3-2 Tsitsipas
Back-to-back holds! Well I never...
Tsitsipas makes Nadal wait on the baseline as he decides he needs a new frame. Nadal raises his eyebrow when the Greek finally returns, giving him an 'are you ready now?' type glare.
Tsitsipas holds
*Nadal 6-4 4-6 3-2 Tsitsipas
Acceptable in the 80s and more than acceptable now for Stefanos Tsitsipas. The Greek changes tack as he decides to hit Nadal with some serve-volleying, a tactic which works out well as he holds relatively comfortably.
Nadal holds
Nadal 6-4 4-6 3-1 Tsitsipas*
Nadal's serving stats have plummeted quicker than the mercury in a thermometer lobbed into the freezer.
The Spaniard is facing another sticky situation as he trails 0-30, before landing only his second first serve of the set to help him stem the tide.
That gives him the confidence to start landing more of his first attempts - targeting the Greek's backhand - and it gets him over the line.
Post update
Russell Fuller
BBC tennis correspondent at the O2 Arena
The shape of the match has disappeared completely.
Nadal breaks
*Nadal 6-4 4-6 2-1 Tsitsipas
This has suddenly gone bonkers. Nadal strikes straight back with a hold to love.
No idea what has happened. The two men who were serving with such dominance in the first two sets have seemingly been replaced by a couple of blokes from the Isle of Dogs.
Post update
Russell Fuller
BBC tennis correspondent at the O2 Arena
Anyone's guess who is going to win this match and qualify for the semi-finals.
Tsitsipas breaks
Nadal 6-4 4-6 1-1 Tsitsipas*
Apostolos Tsitsipas almost loses his face mask such is the vigour with which he jumps to his feet. Dad is happy because son has claimed that break straight back.
Live Reporting
Jonathan Jurejko
All times stated are UK
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Latest PostGoodbye!
Well, that was fun! And we've got to do it all again tomorrow. Can. Not. Wait!
The big one is Novak Djokovic against Alexander Zverev at 14:00 GMT, which you can watch live on BBC Two.
We will also have live text of that match, which means I might have to do a cover of the Abba turn at the very start of tonight's coverage.
Because that match, chiquitas and chiquitos, is also winner takes it all...
Thanks for your company tonight. Sithee tomorrow!
Post update
Nadal 6-4 4-6 6-2 Tsitsipas
An indication of how tough it was for Stefanos Tsitsipas tonight...
Post update
Nadal 6-4 4-6 6-2 Tsitsipas
In case you missed it earlier, Nadal will play Daniil Medvedev in Saturday's semi-final.
Medvedev, who lost to Nadal in a humdinger of a US Open final in September 2019, is assured of his place as the Group Tokyo 1970 winner.
World number one Novak Djokovic and Alexander Zverev battle it out for the right to face Dominic Thiem - who beat Nadal to top Group London 2020 - in the other semi-final.
'Reaching the semi-finals is very important'
Nadal 6-4 4-6 6-2 Tsitsipas
Rafael Nadal on reaching the ATP Finals semi-finals: "I think I played quite well for such a long time. That game at 5-4 in the second set affected me a little bit, but then I was able to get the break early in the third, then he broke me and I broke again.
"I was winning serves quite comfortably until that moment, after that everything changed and I started to serve worse.
"But in general terms it was a positive match for me. To reach the semi-finals in the last tournament of the year is an important thing."
Post update
Nadal 6-4 4-6 6-2 Tsitsipas
As always, Rafa doesn't rush as the microphone waits. A change of shirt, a dig around for the facemask and the bull-emblazoned tracky top. Now he is ready...
Post update
Nadal 6-4 4-6 6-2 Tsitsipas
Not to be for Stefanos Tsitsipas, who was aiming to become the first man to defend the title since Novak Djokovic in 2015.
While the impressive win against Andrey Rublev gave him hope, it was not to be with Dominic Thiem and now Rafa Nadal in tip-top shape.
Game, set and match Nadal
Nadal 6-4 4-6 6-2 Tsitsipas
Keep that space in the trophy cabinet ready and waiting...
Rafa rolls on! Nadal moves into the semi-finals as he looks to bag the ATP Finals title for, quite staggeringly, the first time.
The Spaniard seals his spot in the last four with a precise winner down the line. The grin accompanying his sideward glance at his box tells you exactly how he is feeling. Vamos!
Match point to Nadal
*Nadal 6-4 4-6 5-2 Tsitsipas
Ooof! A thumping ace down the middle puts Nadal within touching distance of the match... only for Tsitsipas to force deuce when Nadal drifts a return wide.
On we go...
Post update
*Nadal 6-4 4-6 5-2 Tsitsipas
Superb craftsmanship from Nadal, constructing the point beautifully and putting away a volley for 15-30. From that delicate touch, he goes to some hammer blows in the next point and Tsitsipas goes long for 30-30.
Post update
*Nadal 6-4 4-6 5-2 Tsitsipas
Hang on... Tsitsipas is not heading to the cloakroom and grabbing his coat just yet. The Greek asks a question of Nadal at 0-30...
Nadal serves for the match
*Nadal 6-4 4-6 5-2 Tsitsipas
So then, here we are. After the rollercoaster ride at the start of this set, Rafael Nadal is coasting towards the platform.
The Spanish second seed serves for the match - and his spot in the semi-finals.
Nadal breaks
*Nadal 6-4 4-6 5-2 Tsitsipas
Not only is Nadal serving better, he is still returning sharply. That, combined with Tsitsipas losing his way, racks up two break points and he takes the second one when Tsitsipas sprays a wild one with more force than a jet-wash operative.
Nadal holds
Nadal 6-4 4-6 4-2 Tsitsipas*
Remember when Nadal was holding serve comfortably and quickly? Yes, that. The world number two moves a step closer to the magic number with a blink-and you'll-miss-it hold to love.
The tornado which swept through the O2 and demolished a number of serves seems to have passed. Nadal is emerging from the wreckage and rebuilding quickly.
Post update
*Nadal 6-4 4-6 3-2 Tsitsipas
Back-to-back holds! Well I never...
Tsitsipas makes Nadal wait on the baseline as he decides he needs a new frame. Nadal raises his eyebrow when the Greek finally returns, giving him an 'are you ready now?' type glare.
Tsitsipas holds
*Nadal 6-4 4-6 3-2 Tsitsipas
Acceptable in the 80s and more than acceptable now for Stefanos Tsitsipas. The Greek changes tack as he decides to hit Nadal with some serve-volleying, a tactic which works out well as he holds relatively comfortably.
Nadal holds
Nadal 6-4 4-6 3-1 Tsitsipas*
Nadal's serving stats have plummeted quicker than the mercury in a thermometer lobbed into the freezer.
The Spaniard is facing another sticky situation as he trails 0-30, before landing only his second first serve of the set to help him stem the tide.
That gives him the confidence to start landing more of his first attempts - targeting the Greek's backhand - and it gets him over the line.
Post update
Russell Fuller
BBC tennis correspondent at the O2 Arena
The shape of the match has disappeared completely.
Nadal breaks
*Nadal 6-4 4-6 2-1 Tsitsipas
This has suddenly gone bonkers. Nadal strikes straight back with a hold to love.
No idea what has happened. The two men who were serving with such dominance in the first two sets have seemingly been replaced by a couple of blokes from the Isle of Dogs.
Post update
Russell Fuller
BBC tennis correspondent at the O2 Arena
Anyone's guess who is going to win this match and qualify for the semi-finals.
Tsitsipas breaks
Nadal 6-4 4-6 1-1 Tsitsipas*
Apostolos Tsitsipas almost loses his face mask such is the vigour with which he jumps to his feet. Dad is happy because son has claimed that break straight back.