Geophysical hazards such as tsunamis, storm surges, debris flows, and landslides pose a significant risk to a large fraction of the world's population. Mathematical models and computer simulations of these hazards are critical in developing a better understanding of past events, both recent and pre-historic. They are also used to assess hazards, issue real-time warnings, and help communities prepare – despite the uncertainties surrounding potential future disasters. This lecture will explore some of the ways that mathematics plays an important role in the development of models, software, and probabilistic hazard assessment.