Arroyo was born in Bilbao in 1964 and graduated as an architect and town planner in 1988 from the ETSAM in Madrid. Since then, he has taught and lectured worldwide. His firm, NO.MAD, was founded in Amsterdam in 1989, moved to Paris and Bilbao, and has been based in Madrid since 1996. The firm's work has been published and exhibited in several languages. Essential works include the Lasesarre Football Stadium, the Levine House, the Sondika Kindergarten, the Desierto Square, the Arquia Bank and the Zafra-Uceda House, among others.