Liverpool were paired with Chelsea in the Champions League for the fifth time in five years yesterday, while Barcelona were matched against Bayern Munich in another quarter-final.
Defending champions Manchester United will face FC Porto, who knocked United out in 2004 when Jose Mourinho was in charge of the Portuguese team and took it all the way to the title.
Arsenal play Villarreal in a repeat of the 2006 semi-final which the Gunners won before losing to Barcelona in the final.
The first legs will be played 7-8 April and the second legs on 14-15 April.
Liverpool and Chelsea have already played each other 22 times in five years in all competitions.
"We know each other very well and this is an exciting draw," said Liverpool manager Rafa Benitez, who led the team to its memorable 2005 triumph and also to the 2007 final where they lost to AC Milan.
"We knew it would be difficult to avoid an English team but we need to approach the two games with confidence. We've done the double over them this season in the league but clearly these two games in the quarterfinals will be different."
Chelsea coach Guus Hiddink won the European Cup with PSV Eindhoven in 1988.
"I'm OK with the draw," he said. "If you have the great desire to go to the end in May you have to play the big teams, whether it's Liverpool or Manchester United or Barcelona. Whichever, there's a lot of attention worldwide which is good for football."
In the semi-finals, Man United or Porto will face Villarreal or Arsenal, and Barcelona or Bayern Munich will meet Liverpool or Chelsea.
That sets up the possibility of another all-English final. Manchester United beat Chelsea on penalties in last year's final in Moscow. The two teams, currently first and second in the Premier League, could meet again in Rome on 27 May.
The Liverpool-Chelsea second leg will be on 14 April to avoid a clash with the 20th anniversary of the Hillsborough disaster on 15 April.
Barcelona, who lead the Spanish league by six points, have won the European title only twice but the last time was in 2006 when they beat Arsenal. Bayern have won it four times, the last being in 2001.
"That's a heck of a draw, it's something quite extraordinary," Bayern coach Juergen Klinsmann said. "It's a great challenge to be measuring up against the best team in Europe right now."
The first legs of the semi-finals will be played on 28-29 April and the return legs on 5-6 May.
Manchester United manager Alex Ferguson welcomed the matchup bearing in mind his team avoided tougher opponents such as Barcelona and Bayern, who crushed Sporting Lisbon 12-1 on aggregate to reach the quarter-finals.
"This is a good draw for us," Ferguson said. "We've met Porto before and obviously we respect any Portuguese team. We have had a huge Portuguese influence in the club firstly with Carlos Queiroz but now with Cristiano Ronaldo and Nani so we understand Portuguese football."
Vitor Baia, the Porto goalkeeper in that title-winning season and now the club's head of foreign relations, said his team would not be scared of the defending champions.
"We're going up against one of the best clubs in the world but that doesn't mean we'll be giving up," Baia said. "We have something to bring to this game. We have shown our quality and our character by coming this far."
Arsenal should be favourites against Villarreal but manager Arsene Wenger believes it will be a tough round.
"It is maybe a good opportunity to play the first game away from home," he said. "It will depend on the quality of your performance and the players available as well. We have learned that to knock any Spanish team out is very difficult."
Quarter-finals (7-8 April/14-15 April)
Villarreal-Arsenal
Man.United-FC Porto
Liverpool-Chelsea
Barcelona-Bayern M.
Semi-finals (28-29 April/5-6 May)
Barcelona or Bayern M.- Liverpool or Chelsea
Man.United or FC Porto-Villarreal or Arsenal