You can read the full report on Roger Federer's victory over Dominic Thiem on our website.
That's all from me today but you can join me tomorrow at around 13:45 GMT for build-up to Novak Djokovic's match with Alexander Zverev.
Who can qualify tomorrow?
After Federer's victory tonight, Kevin Anderson has not quite made it into the semi-finals but Novak Djokovic or Alexander Zverev could tomorrow.
World number one Djokovic will if he defeats Zverev and Marin Cilic loses to John Isner. A three-set win for Cilic would also see him through.
Zverev needs to beat Djokovic and hope John Isner either defeats Cilic in three sets or loses.
What's on tomorrow?
BBC Two
We have more tennis action tomorrow as Group Guga Kuerten take to the court.
Tournament favourite Novak Djokovic is in action against Alexander Zverev and you can watch that match live on BBC Two from 14:00 GMT.
Marin Cilic v John Isner follows and you can listen to BBC Radio 5 live from 20:00-23:00 and on BBC Radio 5 live sports extra (online only).
'I was more positive today'
Roger Federer speaking to Sky Sports: "It feels good. I am very happy that I showed a reaction after the last match.
"No match is easy here. It is not something I'm used to - losing then coming back to play. Dominic [Thiem] is a great guy and has one of the best backhands in the game.
On needing a positive attitude: "Against Kei [Nishikori], it was 4-4 in the first set and we were both playing very badly. Instead of seeing things positively, I thought negatively. It was disappointing but it happens and Kei played well at the end to make it hard for me.
"Today I was more positive and happy on the court. I love playing in London and I had to remind myself what a privilege it is. I hope I showed it.
On his next match against Kevin Anderson: "I hope it is not a match like Kevin Anderson played this afternoon! It is never easy to play against him, especially indoors. I am happy I am getting a chance to play him again and have a re-match [from Wimbledon.]
ReutersCopyright: Reuters
Post update
You don't write off Roger Federer.
Game, set and match
Federer 6-2 6-3 Thiem
Federer loses out in the rally, sending his backhand into the net. Deuce.
But he takes the advantage with an unstoppable one-handed shot down the line and Federer goes on to break and win the match as Thiem sends his forehand wide.
Getty ImagesCopyright: Getty Images
Post update
Simon Briggs
Daily Telegraph tennis correspondent on BBC Radio 5 live sports extra
A well-constructed point from Thiem. I haven't seen him do that too often today.
Match point Federer
Federer 6-2 5-3 Thiem*
Thiem's knees hit the ground as he tries to return a short ball, only to find the net. He bounces back with a delicate half-volley and Federer's forehand return is then inches away from the lines - confirmed by a challenge.
A 32nd unforced error brings up match point for Federer...
Federer holds
Federer 6-2 5-3 Thiem*
Federer is starting to look more like himself now. A few flicked forehands set up a winner before Thiem slices a backhand way into the stands.
Another ace seals the game. Easy.
Getty ImagesCopyright: Getty Images
Thiem holds
*Federer 6-2 4-3 Thiem
An ace starts the game off nicely for Thiem and another strong serve forces Federer to send his backhand wide.
He rounds the game off with a thumping wide serve and Federer's return goes sailing over the baseline.
PACopyright: PA
Post update
Federer 6-2 4-2 Thiem*
Thiem's average service game has been three minutes and 55 seconds.
Federer's has lasted only one minute 43 seconds on average.
Federer holds
Federer 6-2 4-2 Thiem*
Federer quickly marches up to 40-0 with some well-placed second serves. But Thiem drops a lovely short slice and smashes a forehand past the space left by Federer's run into the centre.
Federer holds serve with another neat serve.
Getty ImagesCopyright: Getty Images
Post update
Russell Fuller
BBC tennis correspondent at the O2 in London
The way he is playing, it is almost inconceivable that Federer won't be in the semis.
Thiem holds
*Federer 6-2 3-2 Thiem
Federer does incredibly well to reach a fizzing forehand from Thiem but the Austrian ends the rally with a volley at the net. Deuce.
Thiem takes the advantage with a deep forehand with top spin and holds with an ace.
Break point Federer
Federer 6-2 3-1 Thiem*
Thiem does the hard bit to set up the winner but overcooks his forehand again. Break point Federer.
Post update
Federer 6-2 3-1 Thiem*
Federer pushes Thiem deep behind the baseline and forces his forehand long. But Thiem punishes him with a superb forehand winner into the corner to move up to 40-15.
The Austrian then slices a low chip into the net and sends another forehand into the same spot. Deuce.
Post update
Simon Briggs
Daily Telegraph tennis correspondent on BBC Radio 5 live sports extra
Let's face it, this tournament needs Federer to have a good showing, it hasn't really caught light yet.
Federer holds
Federer 6-2 3-1 Thiem*
Federer catches Thiem off balance and sends a forehand into the gap. Thiem's wide return then luckily hits the net but Federer reaches it and wins the point.
He serves the game out with a subtle drop shot and Thiem's stretched backhand goes sailing over the sidelines.
ReutersCopyright: Reuters
Thiem holds
*Federer 6-2 2-1 Thiem
This time Federer plants his backhand return into the net and Thiem moves up to 30-15. The Austrian then executes a lovely cross-court shot and Federer's too slow to react. He finishes it off with a pacey serve which Federer can't return in play.
Get Involved
#bbctennis
Adam Haigh: Yesterday Ronaldo was at the O2, today we have Alex from Love Island. Ying and yang i suppose.
Former England cricketer Alec Stewart is also in the house!
Live Reporting
Emma Sanders
All times stated are UK
Get involved
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Getty ImagesCopyright: Getty Images 
Getty ImagesCopyright: Getty Images 
PACopyright: PA 
Getty ImagesCopyright: Getty Images 
ReutersCopyright: Reuters 
Getty ImagesCopyright: Getty Images
Latest PostPost update
You can read the full report on Roger Federer's victory over Dominic Thiem on our website.
That's all from me today but you can join me tomorrow at around 13:45 GMT for build-up to Novak Djokovic's match with Alexander Zverev.
Who can qualify tomorrow?
After Federer's victory tonight, Kevin Anderson has not quite made it into the semi-finals but Novak Djokovic or Alexander Zverev could tomorrow.
World number one Djokovic will if he defeats Zverev and Marin Cilic loses to John Isner. A three-set win for Cilic would also see him through.
Zverev needs to beat Djokovic and hope John Isner either defeats Cilic in three sets or loses.
What's on tomorrow?
BBC Two
We have more tennis action tomorrow as Group Guga Kuerten take to the court.
Tournament favourite Novak Djokovic is in action against Alexander Zverev and you can watch that match live on BBC Two from 14:00 GMT.
Marin Cilic v John Isner follows and you can listen to BBC Radio 5 live from 20:00-23:00 and on BBC Radio 5 live sports extra (online only).
'I was more positive today'
Roger Federer speaking to Sky Sports: "It feels good. I am very happy that I showed a reaction after the last match.
"No match is easy here. It is not something I'm used to - losing then coming back to play. Dominic [Thiem] is a great guy and has one of the best backhands in the game.
On needing a positive attitude: "Against Kei [Nishikori], it was 4-4 in the first set and we were both playing very badly. Instead of seeing things positively, I thought negatively. It was disappointing but it happens and Kei played well at the end to make it hard for me.
"Today I was more positive and happy on the court. I love playing in London and I had to remind myself what a privilege it is. I hope I showed it.
On his next match against Kevin Anderson: "I hope it is not a match like Kevin Anderson played this afternoon! It is never easy to play against him, especially indoors. I am happy I am getting a chance to play him again and have a re-match [from Wimbledon.]
Post update
You don't write off Roger Federer.
Game, set and match
Federer 6-2 6-3 Thiem
Federer loses out in the rally, sending his backhand into the net. Deuce.
But he takes the advantage with an unstoppable one-handed shot down the line and Federer goes on to break and win the match as Thiem sends his forehand wide.
Post update
Simon Briggs
Daily Telegraph tennis correspondent on BBC Radio 5 live sports extra
A well-constructed point from Thiem. I haven't seen him do that too often today.
Match point Federer
Federer 6-2 5-3 Thiem*
Thiem's knees hit the ground as he tries to return a short ball, only to find the net. He bounces back with a delicate half-volley and Federer's forehand return is then inches away from the lines - confirmed by a challenge.
A 32nd unforced error brings up match point for Federer...
Federer holds
Federer 6-2 5-3 Thiem*
Federer is starting to look more like himself now. A few flicked forehands set up a winner before Thiem slices a backhand way into the stands.
Another ace seals the game. Easy.
Thiem holds
*Federer 6-2 4-3 Thiem
An ace starts the game off nicely for Thiem and another strong serve forces Federer to send his backhand wide.
He rounds the game off with a thumping wide serve and Federer's return goes sailing over the baseline.
Post update
Federer 6-2 4-2 Thiem*
Thiem's average service game has been three minutes and 55 seconds.
Federer's has lasted only one minute 43 seconds on average.
Federer holds
Federer 6-2 4-2 Thiem*
Federer quickly marches up to 40-0 with some well-placed second serves. But Thiem drops a lovely short slice and smashes a forehand past the space left by Federer's run into the centre.
Federer holds serve with another neat serve.
Post update
Russell Fuller
BBC tennis correspondent at the O2 in London
The way he is playing, it is almost inconceivable that Federer won't be in the semis.
Thiem holds
*Federer 6-2 3-2 Thiem
Federer does incredibly well to reach a fizzing forehand from Thiem but the Austrian ends the rally with a volley at the net. Deuce.
Thiem takes the advantage with a deep forehand with top spin and holds with an ace.
Break point Federer
Federer 6-2 3-1 Thiem*
Thiem does the hard bit to set up the winner but overcooks his forehand again. Break point Federer.
Post update
Federer 6-2 3-1 Thiem*
Federer pushes Thiem deep behind the baseline and forces his forehand long. But Thiem punishes him with a superb forehand winner into the corner to move up to 40-15.
The Austrian then slices a low chip into the net and sends another forehand into the same spot. Deuce.
Post update
Simon Briggs
Daily Telegraph tennis correspondent on BBC Radio 5 live sports extra
Let's face it, this tournament needs Federer to have a good showing, it hasn't really caught light yet.
Federer holds
Federer 6-2 3-1 Thiem*
Federer catches Thiem off balance and sends a forehand into the gap. Thiem's wide return then luckily hits the net but Federer reaches it and wins the point.
He serves the game out with a subtle drop shot and Thiem's stretched backhand goes sailing over the sidelines.
Thiem holds
*Federer 6-2 2-1 Thiem
This time Federer plants his backhand return into the net and Thiem moves up to 30-15. The Austrian then executes a lovely cross-court shot and Federer's too slow to react. He finishes it off with a pacey serve which Federer can't return in play.
Get Involved
#bbctennis
Adam Haigh: Yesterday Ronaldo was at the O2, today we have Alex from Love Island. Ying and yang i suppose.
Former England cricketer Alec Stewart is also in the house!