Phytoplankton are composed of diverse taxonomical groups, which are manifested as distinct morphology, size and pigment composition. These characteristics, modulated by their physiological state, impact their light absorption and scattering, allowing them to be detected with ocean color satellite radiometry. There is a growing volume of literature describing satellite algorithms to retrieve information on phytoplankton composition in the ocean. This synthesis provides a review of current methods and a simplified comparison of approaches. The aim is to provide an easily comprehensible resource for non-algorithm developers, who desire to use these products, thereby raising the level of awareness and use of these products and reducing the boundary of expert knowledge needed to make a pragmatic selection of output products with confidence. The satellite input and output products, their associated validation metrics, as well as assumptions, strengths and limitations of the various algorithm types are described, providing a framework for algorithm organization to assist users and inspire new aspects of algorithm development capable of exploiting the higher spectral, spatial and temporal resolutions from the next generation of ocean color satellites.