Napoli crashed out of the Europa League round of 32 on Thursday, while Arsenal and Borussia Dortmund overcame scares and Atletico Madrid and AC Milan easily advanced.
Serie A leaders Napoli were knocked out on away goals despite a 2-0 win away to RB Leipzig on Thursday.
The German side advanced by the slimmest of margins after surprising Napoli 3-1 in the first leg in Italy last week.
Despite their domestic league concerns, Napoli started a strong lineup with Marek Hamsik, Dries Mertens and Lorenzo Insigne.
Piotr Zielinski tapped in a rebound in the first half, and Insigne struck in the 86th minute to provide some hope, but a third goal would not come despite Napoli putting eight shots on target.
Borussia Dortmund appeared to be following into the exit until Marcel Schmelzer scored in the 83rd minute to secure a 1-1 draw at Atalanta.
Rafael Toloi scored in the 11th minute to put the hosts ahead on away goals after a 3-2 Dortmund win in the first leg, but Schmelzer popped up to score after Atalanta keeper Etrit Berisha fumbled Marco Reus' scuffed shot into his path.
Arsenal held on to advance 4-2 on aggregate despite losing 2-1 at home to Swedish side Ostersunds.
Arsene Wenger started Rob Holding and Jack Wilshere after the comfortable 3-0 victory in Sweden last week, but two Osterunds goals in two minutes put the Gunners on edge early.
Racing back to cover an open goal, Calum Chambers redirected Hosam Aiesh's shot from an angle straight into the Arsenal net, and Osterunds stunningly went 2-0 up on the day just seconds later, when Ken Sema settled a long pass in the box, shook himself free of a defender and lashed his left-footed shot into the far corner.
However, Arsenal hit back immediately after half-time to secure the tie, Sead Kolasinac lashing home from close range after a failed clearance of a Hector Bellerin chipped cross into the box.
Kevin Gameiro scored Atletico Madrid's only goal as a 1-0 win over Copenhagen was enough to advance on the back of a big victory last week.
The result appeared out of reach for the visitors after Atletico won 4-1 in Denmark, and Gameiro blasted home a shot from distance in the seventh minute to end any doubt.
Fabio Borini completed AC Milan's triumph over Ludogorets Razgrad, with a 1-0 home victory capping off a 4-0 aggregate win.
Borini scored following a counter-attack in the 21st minute, turning in a Patrick Cutrone cross at the far post.
Ciro Immobile had a hat trick to help Lazio overcome a surprise first-leg defeat to Steaua Bucharest with a comfortable home 5-1 win.
With his team trailing 1-0 after their trip to Romania, Immobile scored either side of a Bastos goal in the first half, and after Felipe Anderson made it 4-0 early in the second half, the striker completed his treble in the 71st minute.
Lyon used their first-leg advantage to move on 4-1 on aggregate at the expense of Villarreal after a 1-0 second-leg victory in Spain.
Jaume Costa was sent off late for the hosts, allowing Lyon space to score the lone goal through Bertrand Traore from close range in the 85th minute.
Celtic were eliminated with a listless 3-0 defeat away to Zenit St. Petersburg undoing their slim first-leg home win.
Branislav Ivanovic and Daler Kuzyaev had turned the tie around within the first half hour, and Aleksandr Kokorin added a third after the hour mark to seal the Russian side's place in the next round.
Lokomotiv Moscow eliminated Mario Balotelli's Nice with a 1-0 win in the second leg to advance 4-2 on aggregate.
Balotelli, who scored twice in the first leg, hit the crossbar twice in early stages, but Igor Denisov scored the lone goal in the 30th minute.
It wasn't all good news for Russian sides, though, as Spartak Moscow came one goal short of forcing extra time despite a 2-1 win at Athletic Bilbao.
After Athletic's Xabier Etxeita cancelled out Luiz Adriano's opener, Lorenzo Melgarejo found a goal in the 85th minute, but the Spanish side held on to win 4-3 on aggregate.
Salzburg also went through 4-3 on aggregate, ousting Real Sociedad with a 2-1 win at home.
Munas Dabbur put the Red Bull club ahead after just 10 minutes, and though Raul Navas soon equalised for the Spanish club he was later sent off with a second booking, allowing Valon Berisha to net a deciding penalty.
Marseille dropped their second leg 1-0 away to Braga but still advanced after a 3-0 home win a week ago. Ricardo Horta slammed home from six yards out for the only goal in Portugal.
Dynamo Kiev barely got through on away goals after a scoreless home draw against AEK Athens, with only their 1-1 draw in Greece last week enough to see the Ukrainian side through.
Bruno Fernandes scored twice to ensure Sporting Lisbon went through despite giving up a late lead in a 3-3 draw over Astana.
The result was mostly in hand after the Portuguese side's 3-1 victory in Kazakhstan last week, and Bas Dost needed only three minutes to add to the lead.
Marin Tomasov gave Astana some hope, but Fernandes' two goals in a 10-minute span after the break sealed the contest on aggregate. However, the visitors didn't give up and Patrick Twumasi scored before Dmitri Shomko equalised on the night following a corner in the 94th minute.
Viktoria Plzen got a 67th-minute goal from Michal Krmenci and a late second from Ales Cermak to beat Partizan Belgrade 2-0 at home and go through 3-1 on aggregate.
CSKA Moscow became the first club to reach the round of 16 on Wednesday by beating Red Star Belgrade 1-0 after a goalless first leg.