To be able to extend the operation of a solar power plant (CSP) up to 15 hours, thermal energy storage (TES) is necessary. But TES also provides more versatility to the plant and makes its reliance during operation hours more dependable. On the other hand, due to the different CSP configurations, a broad spectrum of storage technologies, materials and methods are needed. Sensible and latent heat storage are known technologies in CSP, but thermochemical storage (TCS) is still very much at laboratory level. Nevertheless, TCS has de advantage of nearly no losses during storage and very good volumetric energy density. This review summarizes and compares the different TCS that are today being investigated. Those systems are based in three redox reactions, sulfur-based cycles, metal oxide reduction-oxidation cycles, and perovskitetype hydrogen production, and metal oxide non-redox cycles due to their similarity. This review shows that all these cycles are promising, but none of them seems to have all the characteristics necessary to become the only one storage system for CSP. The main conclusion of the review is that the calcium carbonate is the cycle with most experimentation behind it to infer that it could be viable and should thus be attempted at a research plant scale once a reactivation cycle can be designed; and the manganese oxide cycle, while less developed, is fundamental enough to be a suitable application for desert climates over the rest of the water-frugal or even water-avoiding cycles.