Postpublished at 13:29 BST 27 June 2014
The Djokovic serve comes under attack for the first time in the match, Simon getting to 30-30. But the Frenchman is then forced into two errors thanks to some big Djokovic hitting and we stay on serve.
Andy Murray beats Roberto Bautista Agut 6-2 6-3 6-2 - replay in 'Live Coverage'
Novak Djokovic sees off Gilles Simon 6-4 6-2 6-4 - replay in 'Live Coverage'
Highlights from day three’s matches under the ‘Highlights’ tab
Relive all of the day’s live text updates - they follow below
Tom Fordyce, Mike Henson and Lawrence Barretto
The Djokovic serve comes under attack for the first time in the match, Simon getting to 30-30. But the Frenchman is then forced into two errors thanks to some big Djokovic hitting and we stay on serve.
Legendary broadcaster Terry Wogan is in the Royal Box and already cracking the jokes. I wonder what Tel said to tickle x-rugby player Matt Dawson and the Duchess of Cambridge's mother Carole....
Simon is holding his own out there, the Frenchman relying heavily on his first serve which is working very nicely at the moment. It's another easy service hold and we're back level.
Caroline Wozniacki makes quick work of beating 16-year-old Ana Konjuh 6-3 6-0 in just one hour and nine minutes. The former world number one made just four unforced errors to her opponent's 25.
The 16th seed is the first player to book their place in the second week and has equalled her best performance at Wimbledon to date. The 24-year-old Dane has reached the fourth round three times but never been further.
Djokovic isn't hanging around either, the Serb racing through his service game to love, too. Three games in five minutes - we're flying!
An impressive opening service game from Gilles Simon, the Frenchman racing through to love with an average serve speed of 106mph.
Simon fires a backhand winner down the line to win the opening point of the match, but that's his only real input into a game which is utterly dominated by Djokovic.
Novak Djokovic to serve. Let's do this.
Novak Djokovic was pushed by Radek Stepanek in the previous round, the Serb winning in four sets in a little over three hours. The top seed will want to get through this encounter a bit quicker and save some energy for later in the tournament.
John Lloyd
Former British number one on BBC TV
"Great champions, they don't show it on the court, but they doubt themselves. Even the great ones have little niggly doubts and when you have someone like Boris Becker to tell you what might happen I think it was a great signing for Djokovic. This is Boris' home. It is going to help Djokovic with Boris in his corner in this is the place."
Novak Djokovic and Gilles Simon receive a standing ovation as they stroll out on Centre Court. Meanwhile on Court One, Li Na and Barbora Zahlavova Strycova have started warming up.
Wozniacki is cruising in her third round match against 16-year-old Konjuh, the former world number one leading by a set and a break in the second. Konjuh's first serve percentage is down at 44% while she has failed to convert any of her five break point opportunities.
"Duck!" That's what Kalara Koukalova should have shouted as she got her service action all wrong and hit her doubles partner Monica Niculescu clean in the back of her head. That's got to hurt. Watch it here or via the video console at the top of the page.
Novak Djokovic hasn't lost in the quarter-finals since 2008, when he lost in the second round to Marat Safin. Gilles Simon has only beaten Djokovic once in seven attempts and that was back in 2008.
Pat Cash
1987 Wimbledon champion on BBC Radio 5 live
"Gilles Simon is a very elegant player, very quick. He doesn't have a huge game but there will be a lot of long rallies."
The conditions have improved significantly in the last hour or so, with the clouds dispersing and blue sky appearing. Centre Court is currently bathed in sunshine, which is handy as Novak Djokovic and Gilles Simon are due out shortly.
Feliciano Lopez, who reached the Queen's final earlier this month, is in control over on court 12. The Spaniard, who has made just two unforced errors to Ante Pavic's 11, wins the first set 6-4 1-2.
It's all going smoothly for Fabio Fognini on court 17, the Italian serving out the set 6-4 against Kevin Anderson.
Third seed Simona Halep wraps up the first set 6-3 in 34 minutes as Lesia Tsurenko dumps a forehand volley in the net.
South African Kevin Anderson is receiving his second bit of treatment on his back after 27 minutes of the match. The 20th seed trails Fabio Fognini 5-3 in the first set. The winner of this match will play the winner of Andy Murray v Roberto Bautista Agut.