Postpublished at 22:30
Three English teams in the hat for last 16 draw, which takes place on Monday at 11:00 GMT.
That's all from us tonight, but we'll back on Thursday for some Europa League action. Fun times.
See you later.
Arsenal & Chelsea through to last 16
Giroud's first Arsenal hat-trick
FT: Chelsea 2-0 Porto
Marcano own goal, Willian strike
Round of 16 draw on Monday 14 Dec
Gary Rose
Three English teams in the hat for last 16 draw, which takes place on Monday at 11:00 GMT.
That's all from us tonight, but we'll back on Thursday for some Europa League action. Fun times.
See you later.
Don't let the lack of a smile in this picture fool you, Mesut Ozil is absolutely buzzing after tonight's win. That's his second tweet containing the word 'Ya' in about 10 minutes.
Olympiakos 0-3 Arsenal
Arsene Wenger on 16 successive years of reaching the knockout stages: "I'm proud of consistency because it demands a lot of effort everyday and I think that's what it's about. We escaped, maybe it's a lucky tear for us in the Champions League.
"If you look at the players who were out today and the kind of performance we produced, the performance is absolutely outstanding."
Arsenal reach the knockout stages
The last time Arsenal missed the knockout stages of the Champions League was 1999. It was the year the British minimum wage of £3.60 an hour was brought in.
Arsenal have now reached the last 16 in each of the last 16 years. There's probably some readers of this page who were not alive the last time Arsenal failed to progress.
Uefa.com reporter Paul Saffer highlights the way Roma sneaked through to the last 16. They placed second to Barcelona in Group E.
Arsenal reach the last-16
Olympiakos 0-3 Arsenal
Arsenal manager Arsene Wenger speaks in his news conference: "In the last three weeks we lost Coquelin, Cazorla and Sanchez. With all the other injuries not many people gave us a chance. But we are a real team and you could see that today. To score without conceding a goal is not easy. It is a special night for us. We needed something special and when you can deliver that you can create a positive memory for the rest of the season.
"Maybe it is a lucky year for us in the Champions League, you never know."
To top off a pretty good night for Arsene Wenger, he's also come out on top of our vote, with 84% of you saying he will last longer in his current job than Jose Mourinho.
Wenger thinks this might be Arsenal's lucky year in the Champions League. Here's a bit more from the Gunners boss...
Olympiakos 0-3 Arsenal
Arsenal manager Arsene Wenger: "I told you before that it would be the greatest escape. I must say I'm very proud of the team as we had to be right on the mental and tactical side. At 2-0 we had to push for a third goal, it was too dangerous to stay at 2-0."
On coming back in the group: "Nine times out of 10 you are out. We needed something special to come back like we did and tonight we needed a complete team performance. This team really is a team and they showed it again.
"You don't need to single Giroud out tonight because he scored the goals. But he showed character again with the penalty."
Olympiakos 0-3 Arsenal
Arsenal's hat-trick hero Olivier Giroud reacts on BT Sport: "It's fantastic for me and for the team. We are really pleased. It's nice to go through because we were not in a good position and finally we have done it. We feel relieved tonight.
"In the Champions League it's one level up and we need to be all focused. As a unit, together, good cohesion, defending well and finishing well. It's nice for us. It was not so easy in this stadium with this atmosphere and we are really pleased to have done it.
"We want to go as far as we can. The target is to maybe reach at least the quarter final. It's the fourth year I'm here and we have never played a quarter final. We will have a good rest and open the new page of the Champions League in February."
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Olympiakos 0-3 Arsenal
Arsene Wenger is talking to BT Sport now, and he says Arsenal played "the perfect game". Hard to argue with that.
More from the Gunners boss coming up shortly.
Chelsea 2-0 Porto
Chelsea skipper John Terry: "With our league form being as it is, the fans needed this performance and the players needed it. We gave a big performance, we're delighted.
"In the league I think we have lacked a bit of confidence but not in the Champions League. We have been fluent and dangerous and we saw that again tonight. Now we go to Leicester on Monday, which will be difficult, but we need to try and replicate this performance."
On Monday's last-16 draw: "We're delighted and lot of team will be fearing us. We will see what comes our way. If we can continue form like that this then it can be a springboard."
Chelsea 2-0 Porto
Chelsea manager Jose Mourinho, speaking to BT Sport: "The players were really committed to get a result, as much for their pride. They didn't want to go to the Europa League and especially after the last defeat at home, a second successive defeat would have been an attack to their pride.
"They were compact and always had initiative, they tried to win even when the draw would have been enough. They deserved to win.
"We are not lucky in the Premier League. Luck is part of the game. In the Premier League every detail goes against us and it was a little attack to the players' confidence. It was an important result for the players and the clubs.
"The supporters are unbelievable in their support towards me and I feel sorry I cannot give them more than I am giving them."
#bbcfootball
We know who is through, but who could Arsenal and Chelsea get in Monday's last 16 draw?
Having qualified second in their group, Arsenal could find themselves facing one of Real Madrid, Atletico Madrid, Barcelona, Wolfsburg or Zenit.
Chelsea, meanwhile, have the prospect of a potentially easier last 16 tie, with PSG, PSV, Juventus, Roma, Benfica or Gent their possible opponents.
Olympiakos 0-3 Arsenal
Mark Lawrenson
Former Liverpool defender on BBC Radio 5 live
"When people talk about why do managers let players go like Campbell has been let go a few times it's because at a football club, managers see these players day in day out and they see what we don't.
"They've probably stopped looking at him as a weak link now. You see a young player coming into a team and you are not too sure, you think 'should I give him the ball or not?'
"I do believe after tonight he should go on to become a better player because of the experience."
Group winners: Real Madrid, Wolfsburg, Atleico Madrid, Man City, Barcelona, Bayern Munich, Chelsea, Zenit
Group runners-up: PSG, PSV, Benfica, Juventus, Roma, Arsenal, Dynamo Kiev, Gent.