A place in next season's Champions League remains on offer to the eventual winner of the competition so the stakes at this stage could not be any higher.
United needed a period of extra-time and the decisive intervention of teenage hero Marcus Rashford to defeat Anderlecht in the quarter finals after the tie was left even balanced at 2-2 on aggregate after 180 minutes of action.
Celta were the only team to reach the last four without the need for extra-time or penalties after beating Genk 4-3 on aggregate.
The other semi-final tie will see Ajax take on Lyon.
The Dutch giants were actually beaten 3-2 by Schalke in the second leg of their last eight tie, but managed to hold on to the aggregate lead they had already established to win 4-3 overall after extra-time.
Lyon booked their place in the last four by beating Besiktas 7-6 in a tense penalty shootout in Istanbul after a 3-3 aggregate score-line.
Ajax vs Lyon
Celta Vigo vs Manchester United
First leg ties will be played on Thursday 4th May, with return legs scheduled for a week later. the first team drawn in each tie will play the first leg at home.
The winners of semi-final one (Ajax/Lyon) have also been drawn as the 'home' team for organisational purposes in the final, set for Wednesday 24th May at the Friends Arena.
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