Roma and Villarreal were among the most convincing winners in the Europa League qualifying ties.
On a busy evening in Europe, Roma's 7-1 win at home to MFK Kosice - for a 10-4 aggregate - and Villarreal's 6-1 success against NAC Breda (9-2 on aggregate) caught the eye.
Roma's Francesco Totti scored the first goal of his hat-trick in the opening minute - adding the others in the sixth and 86th minutes - and although the Italians let one in seven minutes before the break, they were soon sure of progressing after a 3-3 draw in the away leg.
Villarreal had lost their first leg 3-1 but put things right in style - thanks to two first-half penalties from Giuseppe Rossi and four other goalscorers. Breda's only goal came from Edwin De Graaf 10 minutes from time.
There were aggregate wins for English clubs Fulham and Everton, 3-2 against Amkar Perm and 5-1 against Sigma Olomouc. But Aston Villa went out on the away goals rule, despite winning 2-1 at home to Rapid Vienna.
Edinburgh club Hearts won 2-0 at home to Dinamo Zagreb, but that was not enough to overturn a 4-0 away-leg deficit.
Among tonight's 38 ties, there were notable victories for PSV Eindhoven (2-0 on aggregate against Bnei Yehuda Tel Aviv after a second 1-0 win at home), Hertha Berlin (after a 3-1 away win at Brondby) and Benfica (5-2 on aggregate, despite losing 2-1 away to Vorskla Poltava).
Galatasaray could only draw 1-1 at FC Levadia Tallinn but had a 5-0 buffer from the home leg.
Steaua Bucharest won 2-1 at St Patrick's Athletic to go through 5-1 on aggregate.
Other teams to progress to the group stages tonight included Shakhtar Donetsk, Basle, Hapoel Tel Aviv, Hamburg, CSKA Sofia, Heerenveen, Sturm Graz, Dinamo Bucharest, FC Twente, Toulouse, AEK Athens, Slavia Prague, Fenerbahce, Ajax, Lazio, Sparta Prague, Genoa, Werder Bremen, Valencia, Athletic Bilbao and Club Brugge - who needed penalties against KKS Lech Poznan.