Fuzzy dark matter (FDM), composed of ultralight bosons, exhibits intricate wave phenomena on galactic scales. Compared to cold dark matter, FDM simulations are significantly more computationally demanding due to the need to resolve the de Broglie wavelength and its rapid oscillations. In this review, we first outline the governing equations and distinctive features of FDM. We then present a range of numerical algorithms for both wave- and fluid-based simulations, discuss their respective advantages and limitations, and highlight representative test problems. To facilitate code comparison, we also provide publicly available initial condition files for both isolated-halo and cosmological simulations.