Thermochemical adsorption heat storage (TAHS) based on hydrated salts can store large amounts of thermal energy at low losses and can be used effectively in industries such as building space heating and domestic hot water. However, pure hydrated salts suffer from low thermal conductivity, and hydrothermal stability such as deliquescence and decomposition under certain conditions. To overcome these drawbacks and increase the heat storage density of the material, its commercialization and widespread practical application was achieved. The impregnation of carbon-based materials with salts is the most used method to achieve efficient TAHS systems. This paper reviews the principles of TAHS for heat storage and the criteria for the selection of adsorption and storage materials. In addition, the common physical parameters for heat storage of pure salt and thermal chemisorption are introduced. Three optimization methods for pore size, composition and system design are presented to address the gaps in the current experiments and applications of thermal chemisorption.