[1] Real Madrid, the most successful of them, have won the European Cup (now known as the UEFA Champions League) on fifteen separate occasions and claimed 32 trophies in total.
Additionally, Deportivo La Coruña have been regulars in the UEFA Champions League, while Athletic Bilbao, Espanyol, Alavés, Zaragoza and Mallorca have all contested major finals in second-tier competitions and below.
Meanwhile, in the UEFA Cup, La Liga had two out of the four semi-finalists, with Barcelona and Alavés, with Liverpool defeating both sides in the semi-finals and final, respectively.
In 2002, La Liga had two out of the four semi-finalists in the UEFA Champions League with Real Madrid beating Barcelona in the semi-finals, then defeating Bayer Leverkusen in the final for a record ninth title.
In 2004, Deportivo La Coruña reached the semi-finals, knocking out defending champions AC Milan in the quarter-finals, but lost to eventual winners Porto.
Meanwhile, in the UEFA Cup, Sevilla followed in Barcelona's footsteps by beating a Premier League side in a European final when they defeated Middlesbrough 4–0.
But a dramatic late equaliser in the second period of extra time from Espanyol's Jonatas took the match to penalties, which Sevilla won for their second UEFA Cup title.
In 2009, Barcelona won the Champions League for a third time, defeating Manchester United in the final 2–0 as part of a first-ever Spanish treble and later a sextuple, becoming the first European side to win six trophies in a calendar year.
In 2010, Atlético Madrid would win the first edition of the newly named UEFA Europa League, overcoming fellow La Liga side Valencia in the quarter-finals, Liverpool in the semi-finals, and defeating Fulham in the final 2–1 after extra time.
That same season, Villarreal reached the semi-finals of the Europa League, beating Napoli, Bayer Leverkusen, and Twente, before being eliminated by eventual winners Porto.
Athletic Bilbao had reached the final by eliminating Manchester United 5–3 in the round of 16 on aggregate, as well as Schalke 04 and Sporting CP in the quarter and semi-finals, respectively.
Real had reached the final by eliminating three German clubs in succession (Schalke 04, Borussia Dortmund and defending champions Bayern Munich).
Barcelona would defeat Italian champions Juventus in the final 3–1, becoming the first European side to win two trebles, while Sevilla overcame Dnipro 3–2 for their second consecutive Europa League title.
The game finished 1–1, and Real Madrid won their eleventh Champions League title after emerging on top after a penalty shoot-out.
After a 3–2 extra time victory over Sevilla in the 2016 UEFA Super Cup, Real eliminated Napoli, Bayern Munich and fellow Spanish semi-finalists Atlético Madrid in the Champions League knockout stage, before defeating Juventus 4–1 in the final.
Although no Spanish side reached the final of the Europa League that season, Celta Vigo managed to make the semi-finals, where they were narrowly eliminated 2–1 on aggregate by eventual winners Manchester United.