Manchester United will play Bayern Munich in the last eight of the Champions League.
United must get past last season's winners over two legs next month to keep alive their chances of winning a trophy in David Moyes' first season.
Chelsea will face Paris St Germain for a place in the last four, while Real Madrid play Borussia Dortmund in a repeat of last season's semi-final and Barcelona have been drawn with La Liga rivals Atletico Madrid.
United and Bayern have plenty of recent history in the competition: the Germans provided the opposition when United completed the treble in 1999, while Bayern were victorious at the quarter-final stage in 2001 and 2010.
The current champions have already beaten Arsenal in this season's knockout stage and finished top of a group featuring Manchester City.
Chelsea, meanwhile, are up against opponents who have joined European football's wealthy elite since the only previous meetings between the clubs in the 2004/5 season.
That was Jose Mourinho's first year in England, and his side won 3-0 in Paris before drawing 0-0 at home in the group stage.
Elsewhere Real Madrid have the added motivation of avenging April's 4-1 hammering in Dortmund which cost them a place in the Wembley final, while Barca and Atletico meet after three drawn games already this season.
Jamie Redknapp says United got the 'worst draw possible' after being paired with Pep Guardiola's Munich troops.
He told Sky Sports: "It's the worst draw possible for United. Bayern are an incredible side and they now have that belief, after winning the Champions League last year, that they can go and beat anybody.
"When they beat Barcelona 7-0 on aggregate last year, it was an incredible night of football and it just shows you the capability they have. David Moyes will have been disappointed with that. It's the toughest draw you wish to have. Anybody's beatable, but at the moment are United capable of doing that? I don't see that happening.
"Arsenal have proved that teams can go there and get results but Bayern look a better side this year. Pep Guardiola has got them pressing, closing and he's taken them to another level. Arjen Robben is a special talent, so is Franck Ribery, then there's Toni Kroos.
"They're not a team like Real Madrid, that has Cristiano Ronaldo or Barcelona, that have Lionel Messi - Bayern are full of stars who work extremely hard for each other and there's not just one player you have to stop.
"United have got nothing to lose, though. All the pressure will be on Bayern."
Meanwhile, Sky Bet make United 3/1 to beat Bayern in the quarter-finals and 28/1 to lift the trophy, while Chelsea are marginal favourites to progress at 4/5 against PSG but both teams can be backed at 11/1 to prevail in Lisbon on May 24.
Sky Bet's head of football trading Paul Wiggins said: "United were already considered the biggest-priced outsiders heading into the draw but their task has just been made significantly more difficult, with holders Bayern considered the side to avoid and odds-on to win the first leg at Old Trafford.
"Chelsea should be reasonably satisfied with both themselves and PSG in the middle of the outright odds before the draw and we consider that one the toughest tie to predict, with the Premier League leaders marginal favourites as they benefit from having the second leg back at Stamford Bridge."
Barcelona v Atletico Madrid
Real Madrid v Borussia Dortmund
Paris St Germain v Chelsea
Manchester United v Bayern Munich
Chelsea travel to PSG on Wednesday 2 April, with the return at Stamford Bridge on Tuesday 8 April. United host Bayern on Tuesday 1 April and travel to Munich for the second leg on Wednesday 9 April.
All ties to be played on April 1/2 and 8/9.
Which Champions League quarter-final tie are you most looking forward to?
Barcelona v Atletico Madrid
Real Madrid v Dortmund
PSG v Chelsea
Man Utd v Bayern Munich