This presentation provides an overview of the subject of numerical modeling of weak shock propagation, with the aim of providing context for subsequent talks in this session. First is a brief history of analytical approaches to the problem of weak shocks in both one and two dimensions, emphasizing the characteristic physical behavior of the solutions. This leads to a discussion of the physical processes that must be modeled, including the Rankine‐Hugoniot conditions at the shock interface, nonlinear steepening, and self‐refraction, refraction and diffraction due to an inhomogeneous medium, dissipation, relaxation, and heating of the medium. Next is a summary of paraxial numerical methods, specifically the NPE and KZK equations, and their recent applications, followed by a description of efforts to develop “wide‐angle” versions of these codes. Computational challenges, and possible approaches, to extending these methods to three dimensions are also presented. Last, a brief introduction to new approaches to 3‐D modeling will be given, along with a discussion of the applicability of computational improvements such as adaptive meshing and parallel processing.