The principles and potential of latent heat storage (LHS) and thermochemical energy storage (TCES) are introduced. LHS is a reliable technology for heat storage over a wide range of temperatures from low to high, and for cold storage such as ice storage. Phase-change material (PCM) development is a key technology for LHS. Technologies for overcoming the major PCM problems of low thermal conductivity and high corrosivity are reviewed. TCES can be operated as a thermally driven chemical heat pump and for heat transformation (upgrading) and cold heat production, and also to store heat with low loss, although TCES has not been commercialized. The principle of heat pump operation is outlined. TCES material generally has low thermal conductivity, and thermal conductivity enhancement methodology and the benefits of the methodology are reviewed.