Their best performance was in the 1982–83 European Cup when they reached the semi-finals, losing narrowly to eventual winners Hamburger SV.

[1][2][3] La Real have thrice competed in the group stages of the UEFA Champions League.

In 2003–04, they qualified directly as runners-up in the previous season's domestic league, and progressed from the group before being beaten by Lyon in the first knockout round.

In 2017, the club competed in the UEFA Europa League groups for the first time after gaining entry directly to that stage, having fallen in the last qualification round three years earlier.

[8] In 2020, La Real appeared to be heading out of the competition at the group stage in the 90th minute of the last matchday, before a goal in stoppage time against SSC Napoli earned them a point, while a goal at almost the same moment in the other fixture meant defeat and elimination for AZ Alkmaar who had been set to go through.