Good afternoon. Serena Williams and Svetlana Kuznetsova should be heading out for their warm-up on Court Suzanne Lenglen in the next few minutes ready for the first of today's quarter-finals at the French Open.

This will be the ninth meeting between these two players, with the world number one having beaten the Russian in six of their eight previous matches.

Of Williams' 15 Grand Slam victories, just one has come at the French . Since her win in 2002, the top seed has reached the semi-finals just once.

Kuznetsova struggled towards the end of 2012, losing in the first round of Wimbledon before withdrawing from the US Open. However, she made a strong start to 2013, reaching the quarter-finals at the Australian Open.

The winner of this match will face the winner of the game that is just getting underway on the Chatrier court. You can follow live text updates from that game with Sport Mole too.

As the players just come to the end of their warm-ups, let's just take a quick look at how they both reaches this stage. It's been a series of easy straight-sets wins for Williams, while Kuznetsova faced a tough second-round encounter with Magdelena Rybarikova, and a tricky fourth-round clash with eighth seed Angelique Kerber.

Right, the players are ready to go, and it's Serena Williams to serve first.

It's a shaky start by the top seed but she manages to hold serve. A couple of early mistakes from Kuznetsova gives Williams a lead, but a good forehand shot from the Russian gets her back into the game. Williams tests her opponent with a volley to take the game to 40-15, and tries the same move on the next point, but this time Kuznetsova is ready, and smashes it back past the American. A double fault brings up deuce, before a poor forehand gives Kuznetsova a chance to break in the opening game. After several more deuces, Williams eventually managed to dig deep to take the game, but she'll need to serve better next time around.

BREAK! Well it may not have been the best service game from Williams, but she looks unstoppable as she returns the Russian's serve, claiming a 40-0 lead with a series of strong forehand strokes to bring up three break points, before a shot to the net from Kuznetsova seals the game for the American.

Williams still looks like she's yet to settle on serve, firing a couple of long balls towards her opponent before smashing her serve into the net. Kuznetsova slides along the baseline as she tries to bring up another break point, but her cross-court forehand goes just long, and Williams is able to take the game with a big serve down the baseline.

Kuznetsova starts the game well, winning the first two points with some well-placed serves, but a stunning return from Williams gets her back into the game. The Russian tries a drop shot, but the top seed sees it coming, and rushes into the net to volley the ball back into the court, but some solid serves allow Kuznetsova to take her first game of the set.

Kuznetsova plays some superb shots from the back of the court, leaving Williams sprinting behind the baseline. However, some impressive play from the net ensures that it's another hold for the world number one. Despite the scoreline, she has been made to work by the Russian in the opening five games of this match.

BREAK! Kuznetsova tries to control a rally from the back of the court, but a mis-hit forehand helps Williams to a 30-0 lead. A good serve helps her get back into the game, but a wide ball brings up two break points for the American. Kuznetsova saves the first, forcing a wide return from her opponent with a good serve, but the top seed gets the better of the Russian in a short rally, and will now serve for the opening set.

Williams takes control of the game with some strong forehand shots, before the first ace of the match gives her two set points, and she seals it with the second ace of the match, claiming the opening set it just 28 minutes.

The scoreline is certainly flattering giving the American's start to the match. Kuznetsova could easily have taken a break in the first game, and made her opponent work hard during all of her service games until the final game of the set.

On a side note, both players have been pretty vocal so far. Neither have quite reached Sharapova or Azarenka levels of grunting, but it's not been far off.

Kuznetsova has had to leave the court for a medical timeout, leaving Williams looking relaxed drinking some water at the side of the court. It's not clear what the problem is for the Russian, she looked to be moving alright until the final game of the opening set.

While we're waiting for Kuznetsova to return to the court, let's have a quick look at some of the stats from the first set. Williams serves two aces and two double faults in her four service games, while Kuznetsova had no aces and just the one double fault.

Kuznetsova jogs back onto the court and grabs her racquet, and she looks ready to go.

Williams makes a couple of unforced errors, finding the net twice, to help Kuznetsova to a 40-15 lead, and the Russian wins the opening game with a brilliants forehand to the corner of the court. Whatever treatment she had seems to have worked.

BREAK! Williams starts the game with her third double fault of the match, before a superb forehand from Kuznetsova just clips the sideline. A long ball lets Williams back into the game before the American gets a lucky strike off the net chord to leave the world number 40 rushing into the net. Another double fault gives Kuznetsova a break point. A strong return from the Russian allows her to take the game, leaving Williams visibly angry herself at the other end of the court.

Williams makes some aggressive returns to bring up two break points, but she wastes the first attempting to smash the ball past Kuznetsova, and instead finds the net. The Russian plays a good forehand from the baseline to take the game to deuce. Kuznetsova seems to have the better of Williams with her forehand, and she makes it count with two well-played points to win the game and consolidate her break.

BREAK! Williams looks really unsettled by Kuznetsova's strong start to this second set. An uncharacteristic shot from the top seed finds the net, but a couple of poor returns from the Russian keep her in the game. Another mis-hit forehand from the American gives Kuznetsova a chance to take another break point. After a lengthy rally, Williams loses her footing sprinting to the corner of the court. She makes the return, but leave the court wide open for Kuznetsova to smash the ball past her.

BREAK! Williams finds some fight as she hits a series of stunning forehand winners to bring up two break points. She gives herself a talking to before preparing to take the first, but it doesn't work, as some brilliantly-timed strokes from the back of the court from Kuznetsova bring up deuce. Williams gets another chance to break as she flicks a backhand volley past the Russian, and wins the game when the Russian hits her forehand into the net.

BREAK! Williams opens the game with an ace, before Kuznetsova sends back a long return. Kuznetsova attacks the Americans second serve, and forces a couple of errors from the world number one to give her yet another break point, and a double fault hands Kuznetsova the game. The Russian will now serve for the set.

BREAK! Some short serves from Kuznetsova allow Williams to attack, and she brings up two break points, but she needs just the one, getting the better of her opponent with a good forehand return. Williams has never looked settled in the second set, but that was one of her better games.

Kuznetsova displays a great range of shots in a lengthy rally to take a 30-0 lead, eventually catching Williams out with a drop shot. The world number one digs deep, running the length of the baseline on more than one occasion to get herself back into the game, which she clinches when Kuznetsova returns the ball to the net. Williams seems to have put her shaky spell behind her, but the Russian has another chance to serve for the set.

Unforced errors are Kuznetsova's downfall early in the game, as she fires the ball well wide to give Williams three break points. However, a couple of well-placed serves save the first two, before an ace with her second serve brings up deuce. Williams reaches high to smash the ball past her opponent, giving her another chance to break, but Kuznetsova returns the game to deuce on the next point. A stunning backhand brings up set point for the Russian. Williams hits the ball into the net while rushing in to return a drop shot, resulting in her first dropped set of the tournament so far.

Kuznetsova had looked to be dropping off the pace towards the end of that set, but securing the levelling set will have given her a confidence boost. It should be a cracking deciding set.

BREAK! Kuznetsova shows some impressive reaction to produce a brilliant drop shot off the back of a powerful forehand from Williams. A careless forehand from the American gives Kuznetsova a chance to break, and she does when the top seed smashes her forehand long.

Williams gets on the attack early on, coming into the net to pounce on a volley, but she gives the ball too much power on the next point, firing her forehand long again. Kuznetsova has not such problems with her forehand, as she sends the ball down the line. Williams appeared to twist her ankle, and is unable to make a return again the next serve, giving Kuznetsova the game. Williams hasn't called for the trainer though, so she seems ok to continue.

If it can go wrong for Williams at the moment, then it is doing. After dropping her first set of the tournament and tweaking her ankle, Williams has to battle with her hair coming loose! It's yet another irritation for the world number one. Kuznetsova takes advantage of her opponents diminishing confidence to force another break point, but she gets too aggressive with her return to take the game to deuce. Williams targets her shots to the Kuznetsova backhand, knowing that she has been struggling against her forehand, to win a 15-stroke rally. The top seed fails to read Kuznetsova's backhand, and is left rooted to the spot as the Russian brings up another break point, but she saves it yet again. Williams eventually forces advantage, and is able to seal the game when Kuznetsova loses her footing and hits the deck.

BREAK! Williams looks strong as she makes a series of stunning returns for force three break points. Kuznetsova saves the first with a brilliant serve, forcing Williams to return the ball wide, but she gets the break on the net point to get the deciding set back on serve.

Williams finally seems to have re-focused at the start of the game, as she gets it underway with an ace, before another powerful serve forces a wide shot from Kuznetsova. The Russian then returns her backhand to the net, but two long balls from the American, following some strong forehand shots from Kuznetsova, get the world number 40 back in this game, before another long shot brings up deuce. Williams finds the net while attempting a forehand to bring up a break point for Kuznetsova, but a long return takes the game back to deuce. Williams finds a big serve to take advantage, before a wide effort from the Russian gives Williams the game. She'll be relieved to have held that after letting a 40-0 lead slip.

We now know that the winner of this match will face Sara Errani in the semi-final, after the Italian beat Agnieszka Radwanska in straight sets.

BREAK! Williams looks back to her best, moving freely around the court to take a 40-15 lead, giving herself two break points. The top seed takes the game with a brilliant forehand to the sideline.

All the momentum is with the world number one now. She claims the opening couple of points with some powerful serves, before Kuznetsova tries to get the better of her with a volley, but the Russian mistakenly leaves the ball, thinking that it is going long. Another big serve following by a shot from the net seals the game for Williams, and she needs just one more to make the last four.

Williams goes on the attack as she looks to avoid serving for the match, but the Russian shows some fight, coming back from 30-15 down to take the game. Williams will now serve for the match.

Serena Williams has two match points.

Williams quickly wins the first two points with some more big serves, but a mis-timed ball toss puts her off to allow Kuznetsova back into the game. However, a strong forehand effort gives the American two match points, and she seals with match by smashing her forehand cross-court, letting out a huge roar as the Russian fails to return it.

Williams is conducting her post match interview in French. She thanks the crowd for their support following a long, difficult match, which she says has left her tired. She pays tribute to her opponent, claiming that the Russian is capable of winning the tournament again, and that the match proves that she is ready for anything.

That's all from the womens' quarter-finals for today. Stick around for reports and reaction from today's matches, as well as live coverage of the men's last eight. Thanks for joining me this afternoon.