Will Gerard Moreno, Pierre-Emerick Aubameyang and Dušan Tadić be the second-leg stars?
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Manchester United, Roma and Villarreal hold leads, and Slavia Praha have a useful away goal, but no team's place in the UEFA Europa League semis looks certain yet.
See what's coming up in the second legs.
Second legs (15 April)
Ole Gunnar Solskjær reminded his side that things might not be quite as rosy as they seemed after a comfortable first-leg win, explaining: "We’ve got three suspensions for the next game, but 2-0 is a very good result." However, debutants Granada may feel they have already given United their best shot after a good performance failed to reap a goal. "I'm very proud of the team, annoyed with the result," said coach Diego Martínez.
First leg: Granada 0-2 Man. United
"We have a chance to finish the job at home," said Slavia boss Jindřich Trpišovský after his team snatched a 1-1 draw, though he will be aware that both of his side's home games in the knockout stage this season ended level. With the UEFA Europa League looking like Arsenal's best chance of a UEFA Champions League place, manager Mikel Arteta knows the situation is a stark one: "The mindset is to win the game; we need to score."
First leg: Arsenal 1-1 Slavia Praha
"I still think we were the better team," said Ajax midfielder Ryan Gravenberch after his side let slip a 1-0 lead to lose their home leg against Roma. "And we still have a chance." Barely daring to dream of a first-ever UEFA competition success, Roma are unbeaten at home in Europe this term (W4 D1), but goalkeeper Pau López – who saved a penalty in Amsterdam – acknowledged that "there's a long way to go still".
First leg: Ajax 1-2 Roma
In the goalscoring form of his life, Gerard Moreno converted the penalty that gave Villarreal the edge in Zagreb, but was happy to share the credit, saying: "Villarreal are putting together an inspirational season." However, Dinamo's success against Tottenham in the last round shows what they can do when apparently all hope is lost. Daily 24sata led its report of the first leg with the headline: "No surrender! We are still in the game, let's press them."
First leg: Dinamo 0-1 Villarreal
First legs (29 April)
Granada / Manchester United vs Ajax / Roma
Dinamo Zagreb / Villarreal vs Arsenal / Slavia Praha
Second legs (6 May)
Ajax / Roma vs Granada / Manchester United
Arsenal / Slavia Praha vs Dinamo Zagreb / Villarreal
Gdańsk Stadium, Poland: 26 May