La Pedrera (Casa Mila)

This undulating beast is another madcap Gaudí masterpiece, built in 1905-10 as a combined apartment and office block. Formally called Casa Milà, it's better known as La Pedrera (the Quarry) because of its uneven grey stone facade which ripples around the corner of Carrer de Provença. The rooftop with its chimney warriors — helmeted sentinels twisted into surreal shapes — is one of Barcelona's most extraordinary spaces.