Sobejano studied at Madrid's ETSAM and took a master's at Columbia. In 1984 he founded Nieto Sobejano Arquitectos with Fuensanta Nieto, with whom he has shared authorship of every project since, from the Madinat al-Zahra museum outside Córdoba to the Moritzburg museum extension in Halle and the C3A in Córdoba itself. He has taught in Madrid and, since 2008, has held a chair in architectural design at the Berlin University of the Arts, where he is also a full member of the Academy of Arts. The practice's recurring device is a cast or carved surface — concrete, stone or brick — pierced with a deep geometric relief that doubles as structure, shading or ornament. He and Nieto received the Aga Khan Award for Architecture in 2010 and the Alvar Aalto Medal in 2015.