We have obtained high resolution group velocity maps of Rayleigh waves at periods from 8 to 25 seconds across the Iberian Peninsula by cross-correlating four months of ambient noise data recorded by 40 permanent broadband stations. Group velocity maps accurately image the main structural elements of the Iberian upper crust, including the Iberian Massif, Alpine orogens and major sedimentary basins. The Pyrenees and the Iberian Chain are imaged as relatively high group velocities, in contrast with the Betic Cordillera, which is characterized by low velocities. We explain these low velocities in the Betics by the presence of widespread intramontane basins created in an extensional episode simultaneous with north-south convergence between the African and Eurasian plates. The most prominent low velocity anomalies in the Iberian Peninsula are related to the Guadalquivir Basin, the flysch units of the Campo de Gibraltar, and the sediments of the Gulf of Cadiz.