The club most recently participated in the 2023–24 Europa Conference League qualifying rounds and reached the play-offs where they were defeated by Aston Villa.

[2] Swedish club Djurgården were their next opponents, but they were unable to play the home match in Stockholm due to adverse winter weather.

[7] After a walkover victory against Swiss club Lausanne,[8] Hibernian faced Spanish giants Barcelona in the quarter-final.

[8] In the return leg at Easter Road, a late penalty kick by Bobby Kinloch gave Hibernian a 3–2 win on the night and a 7–6 victory on aggregate.

Wins against select teams from Copenhagen (Stævnet)[10] and Utrecht[11] put Hibernian into the quarter-finals of the 1962–63 Fairs Cup, where they lost 6–2 on aggregate to Valencia.

[13] Napoli were the league leaders in Italy at the time, had only conceded five goals in their last six matches and had legendary goalkeeper Dino Zoff in their lineup.

[13] Wins against Olimpija Ljubljana[14] and Lokomotive Leipzig[15] in the 1968–69 Fairs Cup pushed Hibernian into a third round tie with Hamburg.

[12] In the final season (1970–71) of the Fairs Cup, Hibernian defeated Malmo 9–2 and Vitoria Guimaraes 3–2, but were then beaten 3–0 by English side Liverpool.

[21] After a 3–2 win in Norway, three goals in four minutes started a 9–1 rout for Hibernian (and a club record defeat for Rosenborg) in the second leg.

[24] A 2–0 home win against Swedish club Öster raised hopes of further progress, but that lead was overturned by a 4–1 defeat in the return leg.

The last of these was in the 1978–79 UEFA Cup, where they defeated Norrkoping 3–2 at home and this lead was preserved as the Swedes were held to a goalless draw in the second leg.

[28] Keith Houchen had missed a penalty kick in the first leg, and this proved costly as Liège scored the only goal of the tie during the additional period.

[30] The first leg in Greece, which was postponed by a week due to the September 11 attacks against the United States,[31] ended in a 2–0 defeat for Hibernian.

[32] Paco Luna missed a chance to score a third and tie-winning goal late in normal time, and the tie entered an extra period.

[32] Despite exiting the competition, the home game against AEK was fondly remembered by the Hibernian supporters; the actor Dougray Scott later named it as his favourite match.

This offered a potential backdoor route into the UEFA Cup, but the fixtures being played in early July meant that Hibernian had to start their pre-season training earlier than other Scottish clubs.

[1] In the opening round, they held Ukrainian club Dnipro Dnipropetrovsk to a goalless draw at home but fell to a 5–1 defeat in the return leg.

[40] They lost 1–0 at home to Danish club Brondby, but a David Gray goal gave Hibernian a 1–0 win in Copenhagen.

[43] After finishing third in the 2020–21 Scottish Premiership, Hibs entered the newly-established Europa Conference League in 2021–22,[44] beating Andorrans Santa Coloma before losing to Croatian side Rijeka.