He was first noticed as a score composer for Spanish films, mostly from Pedro Almodóvar and Julio Medem.

Since then, he has been nominated four times for an Academy Award for his work in the films The Constant Gardener (2005),[1] The Kite Runner (2007), Tinker Tailor Soldier Spy (2011), and Parallel Mothers (2021).

[5][9][10][11][12][13][14] Iglesias also composed the music for Sex and Lucia (2001), directed by Julio Medem[5] and for Oliver Stone's documentary, Comandante (2003).

[5] Iglesias garnered his first Oscar nomination for his score in Fernando Meirelles's film adaptation of The Constant Gardener (2005).

[17] That same year, Iglesias composed the music for Tomas Alfredson's film adaptation of Tinker Tailor Soldier Spy, starring Gary Oldman as George Smiley.