Thermochemical heat storage has the potential to store a large amount of thermal energy from renewables and to cope with the seasonal mismatch of energy demand and supply, ideally without energy losses typical of sensible heat storage. However, in order to have a commercially attractive system, research at material, reactor, and ultimately at system level is still required. The aim of this work is to investigate the current state-of-the-art research at prototype- and system-scale, and to estimate the performance of ideal long-term low-temperature thermochemical storage systems in terms of energy densities and storage capacity costs. First, a review on existing systems based on solid/gas reactions is carried out. Especially for open systems, the choice of adsorbents rather than salt hydrates as active materials is prominent due to their enhanced stability. However, high material costs and desorption temperatures, coupled with lower energy densities, decrease their commercial attractiveness. Then, the performance of ideal open thermochemical heat storage systems based on solid/gas reactions are estimated for different active materials among which salt hydrates, an adsorbent, and an ideal composite. The common reference scenario assumes that the seasonal space heating energy of a passive house has to be stored. The results show that the open system based on a composite material, can represent a valid compromise between hydrothermal stability and storage capacity costs. However, it results in a very large system for the assumed reference scenario conditions. The performances of open systems are then compared with the ideal performance of closed solid sorption systems. The results show that closed systems are in general more expensive and less compact for the assumed reactor layouts. Finally, liquid sorption systems from the literature are compared with the open and closed solid sorption systems. The results show that most of the liquid systems are not able to achieve the minimum temperature required by the consumer in the reference scenario. However, a liquid sorption system based on NaOH-H2O can in principle satisfy the consumer needs and result more compact and less expensive than solid sorption systems based on pure adsorbents and certain salt hydrates. Beside research at material- and reactor-scale, integration of thermochemical storage at grid level has to be investigated to assess its techno-economic feasibility based on their performance and interactions with production and consumption technologies.