United take a 2-0 lead into their quarter-final return with Granada at Old Trafford, while Arsenal head to Slavia Prague with the tie delicately poised at 1-1.
Here, the PA news agency looks at the main talking points.
Yellow peril for United
United cruised to a first-leg win in Spain with Marcus Rashford and Bruno Fernandes on target and Granada offering little attacking threat. The Old Trafford rematch looks a formality for Ole Gunnar Solskjaer's side, with Ajax or Roma awaiting in their last four. But United picked up costly bookings in southern Spain with Luke Shaw, Harry Maguire and Scott McTominay all suspended for the second leg. Could it offer Granada an unlikely route back into the tie?
Time for Rashford rest?
Marcus Rashford's importance to United has been reflected by his impressive statistics this season – 20 goals and 12 assists in 48 appearances. But does the England striker need a rest after being substituted in his last four games? Rashford's first-leg role against Granada was uncertain because of fitness issues, but the 23-year-old still came up with a superb finish to put United in the driving seat. Solskjaer, however, might consider a 2-0 lead good enough to give Rashford a much-needed breather ahead of some key games.
Spotlight on Arteta
The old adage in football says the next game is the most important one and this is certainly true in the case of Arsenal manager Mikel Arteta. A 3-0 weekend win at Sheffield United, while welcome after four games without victory, came against Championship-bound opponents and with Arsenal in the bottom half of the Premier League at kick-off. Arteta has been under fierce scrutiny in recent weeks and the prospect of no European football next season would provide further ammunition for his critics.
Gabriel Martinelli rose to prominence in the Europa League last season with three goals in his first two appearances in the competition. The 19-year-old forward's progress was slowed by a bad run of injuries, but former Gunners defender Martin Keown has been among those calling for the Brazilian to be given more game time. Martinelli made only his fourth Premier League start of the season against Sheffield United and was on target. Could he be the man to upset Slavia hosts who are unbeaten since December and have already knocked Leicester and Rangers out of the Europa League?
Emery reunion hope
Will Villarreal boss Unai Emery get the last laugh on Arsenal? The Spaniard lasted only 18 months at the Emirates Stadium after succeeding Arsene Wenger in May 2018. But Emery could meet his former side with Villarreal holding a 1-0 lead over Dinamo Zagreb after their first-leg win in Croatia. Villarreal and Arsenal are on a Europa League semi-final collision course, and that would hand Emery the perfect opportunity for revenge against his former employers.