The European Cup was the first UEFA tournamanent to be played - back in 1955-56 - and Real Madrid won the first five. It was a single elimination knock-out tournament back then, but was rebranded in 1991-92 as The Champions League when it added in a League Phase to the first round.
Then in 1960 came the Cup Winners Cup, for the winners of each country's major trophy. It was discontinued in 1999.
The UEFA Cup came along in 1971-72 as the third-level European tournament, for the runners up in the various European Leagues. It too took on a facelift in 2009, becoming the Europa League and positioning itself as the second-tier competition.
Finally in 2021 came the new third-level of the cups with the Europa Conference League.