Williams beats Putintseva 5-7 6-4 6-1
Bertens beats Bacsisnzky 7-5 6-2
Djokovic beats Berdych 6-3 7-5 6-3
Thiem beats Goffin 4-6 7-6 6-4 6-1
*Djokovic 6-3 3-1 Berdych
Berdych manages to stop the rot - what a relief for the seventh seed.
He pulls out a plunging ace, an overhead smash and a drop shot as he holds his service game.
The Czech is off the mark in the second set.
#bbctennis and 81111 on text from UK phones
Daniel Woods: "Competing against Djokovic isn't easy, but Berdych looks like he's just glad to be there. Needs to toughen up and start fighting."
Image source, Getty Images
BBC Radio 5 live sports extra
Guardian writer Kevin Mitchell on BBC Radio 5 live sports extra: "Novak Djokovic has got Tomas Berdych pinned like a butterfly. The Czech is forced back behind the baseline and has a look of a beaten man.
"When Djokovic plays like this his game is flawless, pristine."
Djokovic 6-3 3-0 *Berdych
Novak Djokovic hits into the net in a rare, rare error.
Unshaken, he blitzes the rest of his service game - finishing off with a ridiculous drop shot which leaves Berdych shaking his head.
The Czech has only managed to win five points on Djokovic's serve. This could be over very quickly.
*Djokovic 6-3 2-0 Berdych
Djokovic seems to have all the answers to Berdych's questions at the moment.
A cross-court forehand winner leaves Berdych stranded, and he's undone again on the second point. 0-30.
Both men are pinned to their baselines in the longest rally of the game and Djokovic earns three break points with a delightful drop shot.
A double fault hands it to the Serb. He is well up for this now.
BBC Radio 5 live sports extra
Guardian writer Kevin Mitchell on BBC Radio 5 live sports extra: "Novak Djokovic is looking good. You would be a fool to make any of the players in the draw a favourite against him. You need to have an inspired day like Stan Wawrinka did in the final last year."
Image source, ReutersDjokovic 6-3 1-0 *Berdych
Tomas Berdych takes a long, hard look at his box as he hits another forehand into the net. He 's not a happy boy.
Djokovic invites his Czech opponent into a rally at 40-15. The exchange is ended when Berdych hits long past the baseline.
An easy hold for the world number one.
BBC Radio 5 live sports extra
Guardian writer Kevin Mitchell on BBC Radio 5 live sports extra: "You have to be very sure of you placement when you come to the net against Novak Djokovic. If you leave the ball anywhere in his striking zone you are in trouble and that is what happened to Berdych there."
Image source, AP*Djokovic 6-3 Berdych
Danger for Berdych. The world number one is on the prowl.
Djokovic has double set point but he only needs one to take it.
Berdych whacks a forehand into the net and the Serb has the break and set. Simple work in the end.
Image source, APDjokovic 5-3 *Berdych
Berdych playing Djokovic at his own game. The Czech nabs the first point on his opponent's serve.
But it doesn't last.
Berdych can only return Djokovic's hefty serve out wide for 40-15 and the Serb holds with a crowd-pleasing forehand which fizzes straight down court.
Image source, AP#bbctennis or 81111 on text from UK phones
Charlene Beedie: "A quarter final at a Grand Slam....where is the atmosphere?!! Liven up people. My goodness."
Preach.
*Djokovic 4-3 Berdych
Do we have a breakthrough in the opening set?
Djokovic takes the first two points on Berdych's serve, with the Czech hitting long past the baseline for 0-30.
Berdych steals one back but lets out an 'arrrrrgh' when he's forced out wide by Djokovic and his backhand goes awry.
Break point Djokovic. And he snatches it with a forehand.
Image source, APThere are not many famous Austrians.
But tennis is pretty well represented in those that are.
Dominic Thiem is bidding to become the third man for the country to make a Roland Garros semi-final, following Thomas Muster and Jurgen Melzer.
The 22-year-old is 3-2 and a break up on Belgium's David Goffin in the other quarter-final over on Suzanne Lenglen.
Djokovic 3-3 *Berdych
Just like that, Novak Djokovic zips through his service game to love.
I was going to say he hasn't even broken sweat, but he's just had a wipe down with a towel so perhaps I'm exaggerating.
We go level again.
Image source, AP*Djokovic 2-3 Berdych
Tomas Berdych has a brutal forehand - the strongest in the tournament - and he's using it with aplomb.
The Czech moves to 30-15 with the aforementioned forehand winner and he finishes off his service game with an overhead smash down Djokovic's left.
Djokovic 2-2 *Berdych
All by the book so far.
Djokovic holds again, after two flat forehands from Berdych go past the whitewash. Both look cool, calm and collected.
Image source, AP#bbctennis, the BBC Sport Facebook page and 81111 on text from UK phones
Joel Newnham: Good start from #berdych, external serving well. That serve will get him a lot of points in this match
*Djokovic 1-2 Berdych
Tomas Berdych seals the first point of the game with a drop shot which falls a smidge inside the lines in the bottom corner. Very sneaky indeed.
He then serves it out with two thundering aces. Bosh.
Image source, APDjokovic 1-1 *Berdych
I was having a bit of a moan about the emptiness of the Philippe-Chatrier Court yesterday. I think it's even emptier today. Hopefully the atmosphere will improve as the day goes on.
On court, Djokovic uses a nifty drop-shot to lead 40-15 and clips a backhand over the net to hold with relative ease.
Image source, Getty ImagesBBC Radio 5 live sports extra
Guardian writer Kevin Mitchell on BBC Radio 5 live sports extra: "I fear for Tomas Berdych here. He lost 6-0 6-0 to David Goffin at the Italian Open in the build-up to this tournament.
"Djokovic put him away 6-3 6-3 in Miami earlier this year. I think the Czech could be in for a pasting."