After finishing second in their group Celtic have been drawn against 2006 winners Barcelona in the first knockout stage of the Champions League, while fellow runners-up Liverpool and Arsenal both face tough second-leg trips to the San Siro to take on the Milan giants.
Gordon Strachan's side will also play their first-leg at home, where they have an excellent record, but face a daunting trip to the Camp Nou for the return leg.
Liverpool will have to beat Inter Milan if they are to reach their third final in four years. Rafael Benitez's side were second to FC Porto in their qualifying group.
Arsenal also appear to have paid the price for a second place finish, after being drawn against defending champions AC Milan.
Despite their near perfect campaign, however, Manchester United face a stiff test against perennial underachievers and French champions Lyon. The first leg will be in France where Alain Perrin's side have an impressive European record.
Chelsea face Greek side Olympiacos in what looks the easiest possible draw for Avram Grant's men, while Real Madrid will travel to Roma to kick-off their second round challenge.
German side Schalke 04 will host FC Porto before a trip to Portugal and Turkey's Fenerbache face tournament newcomers Sevilla of Spain.
Liverpool, whose form in the knockout phase of the competition has been impressive under Benitez, finished strongly in Group A with a 4-0 win at Marseille but they could manage second after defeats to the French side and Besiktas earlier in their campaign.
Their meeting with the current Serie A leaders will be the first in the Champions League, though the sides met competitively in the 1965 European Cup semi-final, a two-legged contest which Inter won on aggregate.
Celtic are more familiar with their opponents, having played Barca four times in 2004 - twice in the Uefa Cup and twice in the Champions League. The Hoops lost just one of those matches.
Alex Ferguson feels six-times French champions Lyon represent the toughest task Manchester United could have been given.
"Lyon have won the French championship for the last seven years, which is incredible given the number of players they have lost over the last few years," he said.
"It will not be an easy game but hopefully, by the time we get there we will have all our squad available. That is a pre-requisite for the challenge anyway. If I can pick the team I want I think we will have a good chance."
Liverpool will draw on their recent Champions League experience when the time comes for their "very difficult" last-16 tie against Inter Milan, according to manager Rafael Benitez.
"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."
Arsene Wenger insists Arsenal have nothing to fear from their Champions League showdown against AC Milan.
The Gunners have paid a high price for finishing second in Group H after being matched against the defending champions in today's draw for the last 16.
But a defiant Wenger is convinced Arsenal, who were beaten Champions League finalists in 2006, can topple the Italian giants.
"It's an interesting draw. I believe we can do it if we play at our best," he said. "It's a good target for us to get stronger for the match.
"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."
Full draw
Celtic v Barcelona
Lyon v Man Utd
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 19/20 Feb and 4/5 Mar