Mathematical and computational modeling plays an important role in many aspects of risk mitigation for tsunamis and other hazardous geophysical flows (flooding, landslides and debris flows). Modeling these phenomena accurately and efficiently requires specialized numerical methods and software, as they present unique computational challenges. For instance, with tsunami modeling, the vastly different spatial scales between propagation over the ocean and the study of a small region of the coast makes the use of adaptive mesh refinement crucial. Studying inundation requires wetting/drying algorithms that can handle the depth going to zero at the shoreline. Well-balanced methods must be used to accurately capture waves on the open ocean, where their amplitude is very small relative to the fluid depth. Modeling landslides and debris flows requires the development of suitable mathematical models that can account for the complicated internal stresses of a flowing mixture of solid particles and fluid. The spectrum of flows, ranging from landslides and debris flows to tsunamis, are often modeled with depth-averaged equations of which the shallow water equations are the simplest example. Depth-averaged models for landslides requires additional equations to account for the solid volume fraction and pore-fluid pressure. However, these equations present similar mathematical difficulties. I will discuss some of these models, challenges and algorithms. I will also introduce the GeoClaw software, a specialized version of Clawpack that is aimed at solving these real-world geophysical flow problems over topography. I will show results from some recent tsunamis and potential future events, and discuss some of the ways modeling can be used to assess hazards.