This work reviews research activities in the development of phase-change CO2 capture solvents and processes. The focus is on liquid-liquid phase-change solvents where the CO2-lean phase can be recycled to the absorber prior to regeneration hence the energy demands may be substantially decreased compared to non-phase change processes. The review briefly provides the basic chemical and physical principles required to understand the phase-change behavior in post-combustion CO2 capture systems. The reviewed work is further organized per different solvent type into major sections including experimental property measurement studies, experimental pilot plant studies, thermodynamic and kinetic modeling studies as well as process modeling and technoeconomic assessment studies. In all sections we provide details regarding experimental approaches, operating conditions of pilot plants, implementations in different industries and performance data. Key findings include operating observations and performance indicators regarding the investigated solvents and processes as well as a substantiated estimation of their technology readiness level.