Multicolor holography can faithfully record the color, depth, parallax, and other properties of scenes and have thus found numerous applications, for example, in optical document security, nonvolatile data storage, and virtual or augmented reality systems. Nanophotonic metasurfaces present multiple degrees of freedom to manipulate the properties of optical fields at visible wavelengths. These in turn provide opportunities for metasurface-based multicolor holography. We describe recent developments in multicolor metasurface holograms. These are categorized based on their color-separating mechanisms rather than their structural properties, such as whether they are plasmonic or dielectric. We hope this review will provide readers with new insights and thus help extend applications of metasurface-based multicolor holography to other fields.