Arsenal have been paired with reigning Champions League title-holders AC Milan in the draw for the last 16.
Arsene Wenger's side and seven-time winners Milan meet for the first time in this competition, with the first leg at the Emirates Stadium in February.
Celtic face the 2006 winners Barcelona, while Manchester United manager Sir Alex Ferguson will have to guide his side past French champions Lyon.
Liverpool take on Inter Milan and Chelsea are up against Olympiakos.
Manchester United and Chelsea will both have the benefit of playing their second-leg games at home after finishing top of their qualifying groups.
United manager Sir Alex Ferguson described Lyon, who knocked Rangers out in the group phase, as the toughest opponents they could have been drawn against.
"They have won their championship for the last six years now which is an incredible record," he said.
"You never expect easy games at this stage of the European Cup, but hopefully we can navigate that and go on to bigger things. But it's an interesting tie."
Arsenal, Celtic and Liverpool will all hope to set up platforms in their first-leg ties before potentially tricky away trips, having finished second in their groups.
Arsenal manager Arsene Wenger is optimistic that his young side can overcome champions Milan.
"It's an interesting draw," said the Frenchman. "I believe we can do it if we play at our best. It's a good target for us to get stronger for the match.
It's a big one but was it going to be whoever we had drawn
Liverpool chief Rick Parry
"That's achievable because we have plenty of young players who are improving, as we saw against Blackburn in the Carling Cup.
"It's an exciting draw. If you look at last season's results then it's the hardest draw because they are the champions.
"It's a big challenge but if you ask me do we have a chance to knock them out then I say 'yes'.
"After what happened two seasons ago we have a job to do. We must do it the hard way but we're not responsible for the draw.
"If you want to win the Champions League then you have to beat the biggest clubs. AC Milan are a very big team - world and European champions. But we can do it."
AC Milan director Umberto Gandini believes his team have been given the toughest draw.
"Arsenal is probably the worst possible draw we could get," he told BBC Radio Five Live. "Arsenal is an excellent team, very well coached by Arsene Wenger with a lot of young talent.
"But they will be playing against the reigning champions and world (club) champions with some of the best players in the world. It will be a fantastic tie for the fans.
"It is Milan v England, with Inter playing Liverpool."
Liverpool boss Rafael Benitez said his team will draw on the experience of winning the tournament in 2005 and finishing runners-up last year.
We've got a good home record and hopefully that will help us go through
Celtic chief Peter Lawwell
"Everybody was expecting a difficult draw and Inter Milan are one of the top sides," he said.
"They have good players and experience in Europe. It is very difficult but we know the team and we have confidence in ourselves.
"All the teams are difficult to beat but we have some experience of this. Hopefully we will see another of those performances in the knockout stages.
"I think they (Inter) will be worried, for sure. They know we are a good team and anything can happen in two months' time."
Liverpool's opponents will make life as difficult as possible for Benitez's men, according to Inter's chief executive Ernesto Paolillo.
"We feel Liverpool are the strongest team, what better team to have as an opponent?" he said.
"I think Liverpool will make it difficult for us and I hope it will be difficult for them as well.
"The history is in favour of Liverpool but our team has been in good form so I hope we will be in the right condition to win this match."
Meanwhile, Celtic chief executive Peter Lawwell believes that his side's impressive record at home may help them against Catalan giants Barcelona.
"Manager Gordon Strachan has done a fantastic job to get us into the last 16 two years in a row and he will have them prepared," he said. "Bring them on.
"We've got a good home record and hopefully that will help us go through. Any team we got we would be the underdogs. We hope to give a great account of ourselves."
Celtic v Barcelona
Lyon v Manchester United
Schalke v Porto
Liverpool v Inter Milan
Roma v Real Madrid
Arsenal v AC Milan
Olympiakos v Chelsea
Fenerbahce v Sevilla
(Ties to be played on 19/20 February and 4/5 March)