Phase separation is the thermodynamic process that explains how droplets form in multicomponent fluids. These droplets can provide controlled compartments to localize chemical reactions, and reactions can also affect the droplets' dynamics. This review focuses on the tight interplay between phase separation and chemical reactions originating from thermodynamic constraints. In particular, simple mass action kinetics cannot describe chemical reactions since phase separation requires non-ideal fluids. Instead, thermodynamics implies that passive chemical reactions reduce the complexity of phase diagrams and provide only limited control over the system's behavior. However, driven chemical reactions, which use external energy input to create spatial fluxes, can circumvent thermodynamic constraints. Such active systems can suppress the typical droplet coarsening, control droplet size, and localize droplets. This review provides an extensible framework for describing active chemical reactions in phase separating systems, which forms a basis for improving control in technical applications and understanding self-organized structures in biological cells.