Swath-bathymetry and acoustic-backscatter data from the southwest Iberian margin, which hosts the present-day boundary between the European and African plates, reveal the surficial expression of several fault structures <100 km offshore of Portugal. High-resolution and multichannel seismic reflection profiles collected perpendicular to these structures show folding and reverse faulting of the Quaternary units, suggesting present-day tectonic activity. Successive submarine-landslide deposits at the base of the scarps provide evidence of cyclic fault activity. The location and dimension of these newly identified structures agree with the modeled source suggested for the A.D. 1755 Lisbon earthquake and tsunami, possibly the most destructive event in western Europe during historical time. These fault escarpments and deformed seafloor sediments associated with a cluster of shallow seismicity suggest that these thrusts are active and may pose a significant earthquake and tsunami hazard to the coasts of Portugal, Spain, and Morocco.