Join the debate at #bbcfootballpublished at 17:02 Greenwich Mean Time 20 March 2014
Mikey_Hale, external: Man U are riding their luck in all competitions now, if there not careful they're gunna get knocked out in the group stages.
Full-time: Man Utd 3-0 Olympiakos (Agg 3-2)
Man Utd through to quarter-finals
Van Persie scores hat-trick for United
Penalty and free-kick among Van Persie goals
Full-time: Dortmund 1-2 Zenit (Agg 5-4)
Tom Rostance
Mikey_Hale, external: Man U are riding their luck in all competitions now, if there not careful they're gunna get knocked out in the group stages.
A job well done for David Moyes and Manchester United then. Mission make the last eight accomplished.
Can Tottenham continue the good week for English teams in Europe with a win in Lisbon in the Europa League? You'll find out with us - early kick-off in that one. It's a 18:00 GMT kick-off for Tim Sherwood and his boys...
Telegraph sports journalist Henry Winter: "With the result on Sunday losing to Liverpool - any other club would have turned on their manager but in the ground the supporters backed the team and tonight they have been rewarded with a strong performance. This summer is very important it is a short transfer window due to the world cup so they will have to do their business quickly."
Manchester United boss David Moyes: "People will probably think it's a turning point in people's careers but I didn't see it like that because the club don't see it like that. I see myself here for a long time.
"I think we know we have a lot of work to do but it's a great result and we want to stay in the competition. The other teams are good now and we look forward to the draw."
Telegraph sports journalist Henry Winter: "It was looking a bit depressing for English football at the start of the week but I think that it is now encouraging with Chelsea going through, who have the best manager in the country.
"Also Manchester United have got some good players but you only need to look at Real Madrid who could have Gareth Bale or Cristiano Ronaldo running at Patrice Evra - and it could get messy."
Manchester United boss David Moyes: "I'm not feeling any pressure from inside the club, it's coming from you people [the media], we know the job we have to do, it's probably bigger than what I thought when I first came to the club.
"There are stories of this player falling out, or that one falling out, but it's rubbish. People are looking for reasons why we are not doing well but it is only because we have not been playing well."
DSSBrooks:, external Question is, what humiliation awaits in the next round?
Jimmy:, external What's with the negativity? As long as you're in it you can win it. Look at Chelsea in 2012, no one gave them a hope.
Stuart McGhee:, external Great win for United but the fact Giggs was man of the match shows the task left for Moyes to sort out. Still in it though!
Manchester United are still the bookies' outsiders for the Champions League trophy - you can find a best price of 16-1 on a fourth European crown.
Bayern Munich are favourites at 15/8, with Real Madrid a 7/2 shot - while Chelsea can be found at 10-1.
Manchester United boss David Moyes on Ryan Giggs: "It's incredible the amount of games he's played in the Champions League. He was fantastic, the passes he made for the two goals, his general football, he's a freak.
"Ryan is not going to go on forever so we have to find the new Ryan Giggs and use other players but we needed his experience tonight."
Manchester United boss David Moyes on Robin van Persie's injury: "It doesn't look that bad, he's a had a knock in and around the knee area, on the back of his knee. He was great, not many people score a hat-trick in the Champions League."
Telegraph sports journalist Henry Winter: "The most encouraging thing is that David Moyes is saying that Robin van Persie's injury is not too bad. I thought he was terrific tonight. David De Gea's double save was very important, there were touches of Peter Schmeichel about it.
"A positive and a concern arguably is that their most impressive outfield player was a 40-year-old Ryan Giggs. The fans were brilliant and they go into Friday's draw and they will be up against the glitterati.
"They need a Bastian Schweinsteiger figure, a box to box player. The formation he played was two holding players, Michael Carrick and Giggs but where does he play Juan Mata? Mata does not want to play as a right winger, Antonio Valencia isn't a top player but he does a job. A word of praise for Danny Welbeck though who was terrific on the left."
Dortmund captain Sebastian Kehl: "It was not our best match, but we have reached the quarter-finals and can leave with a huge smile on our face.
"We've had a lot of injuries. We never complained. Despite this, we deserve to be among the best eight teams in Europe."
Manchester United boss David Moyes: "The way the players responded after Sunday [pleased me most]. I told the players on Monday morning we have to win 3-0 to give the fans something back. They have been incredible and they deserved it because we've not given them many good nights."
It's back to the drawing board for the Greek champions then. Olympiakos have now lost 18 of their 21 Champions League away games in England, Germany and Spain, keeping only one clean sheet.
Paul in Accrington: Who expected Wigan to beat City in last season's FA Cup and this season's? United could win it as underdogs! They've never been that!
David Moyes says the injury to Robin van Persie is 'thankfully not too bad.' Nothing too serious then.
Mark Lawrenson
Radio 5 live
"The financial men have been sat here tonight and they are thinking how much money do we need to give David Moyes in the summer? And do we trust him with the money? They have a lot to do in the summer.
"The majority of today's players do think of the money, and you have got to sell them Man Utd in a year's time - there is no easy way out, you have to pay them the money. They are going to have to take the hit. The only way to get back into the Champions League is to go out and get better players.
"I wouldn't give Robin van Persie a new contract based on this year's performance so far. He played well tonight but I would say go out and earn it."
It does look like the only way Manchester United will be playing in the Champions League next season is if they win the thing. Could that happen?
Mark Lawrenson
Radio 5 live
"The top four is gone and I think also Man Utd supporters know how much the team has slipped and how much needs to be done. The thing with the Champions League is they can just have a go now. No one will make them favourites."