Here, is a look back at the past meetings between two of the biggest clubs in Europe.
1956-57 European Cup semi-final first leg, April 11: Real Madrid 3 (Rial, Di Stefano, Mateos) Manchester United 1 (T Taylor)
United held Real for an hour but then the Spaniards cut loose with Hector Rial and the great Alfredo di Stefano scoring in quick succession to put the hosts into a clear lead. Tommy Taylor pulled one back for United but almost immediately Enrique Mateos restored the home side's two goal advantage.
Second leg, April 25: Manchester United 2 (T Taylor, Charlton) Real Madrid 2 (Kopa, Mateos)
This was the first European game to be played under floodlights at Old Trafford. Any chance of United advancing had been wiped out before the interval when Raymond Kopa scored the visitors' first before Mateos slammed home a second. Taylor pulled one back 11 minutes after the re-start before Bobby Charlton scored his first European goal near to the final whistle.
1967-68 European Cup semi-final first leg, April 24: Manchester United 1 (Best) Real Madrid 0
By now Real were a shadow of the side which dominated the first five years of the European Cup. Only Gento remained of that illustrious team but they still proved difficult opponents for United to overcome at Old Trafford. It took a goal from George Best to give them a narrow lead to take to Madrid which, as the tie turned out, proved to be crucial.
Second leg, May 15: Real Madrid 3 (Pirri, Gento, Amancio) Manchester United 3 (Zoco og, Sadler, Foulkes)
Real overturned the first-leg deficit inside 40 minutes with Pirri and Gento both scoring to give them an aggregate lead. A Zoco own goal restored United's fortunes, only for Amancio to restore Real's lead right on half-time. David Sadler and long-serving defender Bill Foulkes both found the net in the last 20 minutes to send the Red Devils into the final for the first time.
1999-2000 Champions League quarter-final first leg, April 4: Real Madrid 0 Manchester United 0
Real always looked the more likely scorers and it took a series of fine stops from Mark Bosnich to keep the scoresheet blank for United. Dwight Yorke had a goal ruled out for offside but with home advantage in the second game, the visitors returned to England in optimistic mood.
Second leg, April 19: Manchester United 2 (Beckham, Scholes) Real Madrid 3 (Keane og, Raul 2)
Roy Keane gave Real the advantage when he turned Michel Salgado's cross into his own net. United pushed forward in a bid to get in front but Raul scored twice on the break. David Beckham pulled one back for United but their hopes had long since disappeared by the time Paul Scholes slotted home a penalty two minutes from time.
2002-03 Champions League quarter-final first leg, April 8: Real Madrid 3 (Figo, Raul 2) Manchester United 1 (Van Nistelrooy)
Luis Figo and a double from Raul left United on the brink of a rout in the last eight as Zinedine Zidane inspired Real to be at their ruthless best. Ruud van Nistelrooy scored a crucial away goal to keep United's hopes of progression alive.
Second leg, April 23: Manchester United 4 (Van Nistelrooy, Helguera og, Beckham 2) Real Madrid 3 (Ronaldo 3)
Ronaldo single-handedly wrecked United's Champions League title hopes with a stunning hat-trick. The Brazilian superstar scored an early goal which was cancelled out by Van Nistelrooy before he struck twice again early in the second half. Ivan Helguera's own goal and a double from substitute Beckham was not enough for United as Real finished a breathless match 6-5 winners on aggregate.