The first probabilistic tsunami flooding maps have been developed. The methodology, called probabilistic tsunami hazard assessment (PTHA), integrates tsunami inundation modeling with methods of probabilistic seismic hazard assessment (PSHA). Application of the methodology to Seaside, Oregon, has yielded estimates of the spatial distribution of 100- and 500-year maximum tsunami amplitudes, i.e., amplitudes with 1% and 0.2% annual probability of exceedance. The 100-year tsunami is generated most frequently by far-field sources in the Alaska-Aleutian Subduction Zone and is characterized by maximum amplitudes that do not exceed 4 m, with an inland extent of less than 500 m. In contrast, the 500-year tsunami is dominated by local sources in the Cascadia Subduction Zone and is characterized by maximum amplitudes in excess of 10 m and an inland extent of more than 1 km. The primary sources of uncertainty in these results include those associated with interevent time estimates, modeling of background sea level, and accounting for temporal changes in bathymetry and topography. Nonetheless, PTHA represents an important contribution to tsunami hazard assessment techniques; viewed in the broader context of risk analysis, PTHA provides a method for quantifying estimates of the likelihood and severity of the tsunami hazard, which can then be combined with vulnerability and exposure to yield estimates of tsunami risk.