After completing a degree in history from the University of Lisbon, Costa worked as an assistant for Jorge Silva Melo, Vítor Gonçalves and João Botelho.

He collected the France Culture Award (Foreign Cineaste of the Year) at 2002 Cannes Film Festival for directing In Vanda's Room.

Although continuing to collaborate with non-actors in his later works, he would gradually transition away from the low-resolution documentary style into what critic Armond White characterised as "museum-quality compositions".

In December 2023, alongside 50 other filmmakers, Costa signed an open letter published in Libération demanding a ceasefire and an end to the killing of civilians amid the 2023 Israeli invasion of the Gaza Strip, and for a humanitarian corridor into Gaza to be established for humanitarian aid, and the release of hostages.

[7][8][9] In January 2024, alongside over 300 other filmmakers, producers and actors, Costa signed an open letter against the cuts to the funding of the Argentine film agency INCAA contemplated by the so-called omnibus bill.