Satellite galaxies in groups and clusters play a critical role in the picture of galaxy evolution. As many as a third of all galaxies are satellites, and the quenching of star formation in satellites is the dominant process in building the red-sequence galaxy population at low mass. Furthermore, satellite quenching, and thus color transformation, governs the optical properties of galaxy clusters. I will present an observational and theoretical investigation into the evolution of star formation (and thus color) in satellite galaxies, using the Sloan Digital Sky Survey to examine satellites across a wide range of host halo masses, from massive clusters to the lowest mass dwarf galaxy groups in the local Universe. I will place these results in a fully cosmological context using a high-resolution simulation to track satellite orbits and infall times, showing that the star formation histories of satellites follow a delayed-then-rapid quenching (color transformation) scenario. I also will examine the curious evolution of satellites that orbit beyond the virial radius of their host halo.