Wayne Rooney, Ajax and Fenerbahçe are among the star attractions as the play-off ties get under way; UEFA.com picks out some key facts for all the games.
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AC Milan v Shkëndija
This is a red-and-black derby – the Italian 'Rossoneri' v the Macedonian 'Kuq e Zi'. Italian teams' record in eight UEFA meetings with Macedonian clubs is W6 D2 L0.
Ajax v Rosenborg
Last season's beaten UEFA Europa League finalists, Ajax met Rosenborg in the 2002/03 UEFA Champions League first group stage; the sides drew 0-0 in Trondheim and 1-1 in Amsterdam.
Altach v Maccabi Tel-Aviv
Israeli teams are unbeaten in their last six UEFA meetings with Austrian clubs (W5 D1). Maccabi are on a seven-game European winning streak; Altach are yet to lose in five UEFA away fixtures (W3 D2).
Apollon Limassol v Midtjylland
Midtjylland have bitter memories of their only past tie with Cypriot opponents; they lost to APOEL on away goals in the 2015/16 UEFA Champions League third qualifying round.
BATE Borisov v Olexandriya
BATE's record in four European meetings with Ukrainian sides is D1 L3 – including a 7-0 home defeat by Shakhtar Donetsk in the 2014/15 UEFA Champions League group stage.
Club Brugge v AEK Athens
Club Brugge's record in ten meetings with Greek clubs is W4 D4 L2; AEK are yet to win in ten UEFA encounters with Belgian sides (D6 L4).
Dinamo v Skënderbeu
Dinamo have made a record 101 appearances in UEFA qualifying competitions, and beat Skënderbeu 6-2 on aggregate in the 2015/16 UEFA Champions League play-offs.
Domžale v Marseille
Domžale have won their last six European home games, but have yet to make it to a major group stage. Marseille were losing finalists in the 1998/99 and 2003/04 UEFA Cups.
Everton v Hajduk Split
Wayne Rooney scored his first goal since his return to Everton on Saturday. Hajduk's record in 14 European meetings with English clubs is W3 D2 L9.
FH Hafnarfjördur v Braga
FH are angling to become the first Icelandic side to reach a major UEFA group stage; Icelandic clubs' record in eight UEFA meetings with Portuguese teams is W0 D3 L6 F2 A29.
Krasnodar v Crvena zvezda
Krasnodar midfielder Mihailo Ristić joined the club from Crvena zvezda this summer. Crvena zvezda's record in six UEFA games against Russian clubs is W2 D1 L3.
Legia Warszawa v Sheriff
Legia have not conceded in their last four European home games (W3 D1). Polish clubs' record in six UEFA meetings with Moldovan sides is W3 D1 L2.
Ludogorets v Sūduva
Ludogorets eliminated another Lithuanian side, Žalgiris, in this season's UEFA Champions League second qualifying round. Sūduva have made it through three UEFA rounds for the first time.
Marítimo v Dynamo Kyiv
The journey from Kyiv to Funchal is around 4,300 km. Dynamo's record in 20 UEFA meetings with Portuguese sides is W6 D4 L10.
Osijek v Austria Wien
Osijek have won their three European home games this season without conceding. Austria's record in four UEFA meetings with Croatian sides is W1 D2 L1.
Panathinaikos v Athletic Club
Panathinaikos have not won in their last 14 meetings with Spanish clubs; their overall UEFA record against Liga sides is W3 D7 L17.
PAOK v Östersund
PAOK featured in the last four UEFA Europa League group stages; Östersund have already accounted for Galatasaray in what is their maiden European campaign.
Partizan v Videoton
The sides met in the 1984/85 UEFA Cup third round; Partizan lost 5-0 in Hungary – Jószef Szabó scoring four goals for Videoton – but rallied a little to win the return leg 2-0.
Plzeň v AEK Larnaca
AEK lost to another Czech club – Slovan Liberec – in last season's play-offs, but made it past Mladá Boleslav in the 2011/12 third qualifying round.
Vardar v Fenerbahçe
Macedonian clubs are unbeaten in four UEFA meetings with Turkish sides: W3 D1. Fenerbahçe signed midfield prospect Elif Elmas from Vardar's city rivals Rabotnicki this summer.
Viitorul v Salzburg
Romanian champions Viitorul are owned by national footballing great Gheorghe Hagi. Salzburg's record in six meetings with Romanian sides is W3 D1 L2.
Utrecht 1-0 Zenit
Group stage contenders in 2010/11, Utrecht are now unbeaten in six in Europe (W2 D4). Zenit's record in eight games against Dutch sides has gone to W4 D1 L3 (W3 D1 at home – W1 L3 in the Netherlands).