Traveling waves (TWs) are building blocks for the dynamics of many partial differential equations (PDEs) over unbounded domains, including many PDEs modeling various physical systems. For a number of simple PDEs the occurence and bifurcation of TWs is analytically reasonably well understood. Examples include traveling fronts in (simple) reaction-diffusion problems, or traveling pulses in the KdV equation and in the NLS equation. However, for more complicated systems one often has to resort to numerical methods and to compute approximate TWs. Here, specific problems occur, related to the truncation of the infinite domain, to (possibly) moving meshes, to different ways of 'freezing', to the preservation of symmetries and integrals. Moreover, the spectral and bifurcation analysis of TWs typically requires specific numerical approaches. In this minisymposium we aim to gather recent progress on the bifurcation and numerics of traveling waves in various systems, partly including stochastic effects.