Because of their inaccessibility, submarine landslides are typically studied individually and at great effort and expense to provide knowledge of the specific site conditions where these landslides occur. Statistical analysis of submarine landslide scars can offer generalized perspectives on the processes that initiate submarine landslides and can help toward hazard assessment in areas that have not been studied in detail. The following review discusses more than a decade of development of statistical approaches to studying submarine landslides. Landslides were previously viewed together with other natural hazards, such as earthquakes and fires, as a phenomenon whose size distribution obeys an inverse power law. Inverse power law distributions are the result of self-organized avalanche processes, in which the final hazard size cannot be predicted at the onset of the disturbance. We find that volume and area distributions of submarine landslides along the U.S. Atlantic continental slope and along nine other margins worldwide do not follow an inverse power law. Rigorous statistical tests of several different probability distribution models indicate that the lognormal model is most appropriate for these siliciclastic environments. Lognormal distributions can be simulated by assuming that the area of slope failure depends on earthquake magnitude, in other words, failure occurs simultaneously over the area affected by horizontal ground shaking and does not cascade from nucleating sources. Therefore, the maximum landslide size can be predicted from the earthquake magnitude and the distance from the rupturing fault. Moreover, earthquakes <~M4.5 cannot generate significant submarine landslides. We further demonstrate that empirical, offshore landslide hazard curves can be developed from these lognormal landslide size distributions, if the duration of mapped landslide activity is known. In addition to hazard estimation, scaling relationships can yield insights on the physical processes associated with landslide failure. For example, the log-log relationship between volume and area of landslide scars in siliciclastic margins is observed to be almost linear implying that most landslides are translational. Carbonate margins, in contrast, show a power-law distribution of scar volumes and their volume to area relationship is ~1.3. These results suggest that landslides in carbonate margins are governed by the random distributions of existing fissures, and they act like rock falls on land. Although earthquakes are the principal trigger of submarine landslides, the effects of earthquake frequency on slope stability can be counterintuitive. The average size of landslide scars decreases non-linearly with increasing frequency of earthquakes and increases with increasing sedimentation rate. The effect is interpreted as evidence for densification and shear strength increase of margin sediment, induced by repeated seismic shaking.