The energy consumption in the built environment represents one of the major contributors of carbon emissions to the atmosphere. This leads to the need for a transition in the building sector and the introduction of policies that pursue high efficiency in residential and non-residential buildings with an increasing share of renewables. The benefit of the use of thermal energy storage is widely recognized to increase the efficiency of energy systems in different building typologies, to help in the introduction of renewable energies in buildings and to reduce the energy demand needed for heating and cooling. Nowadays, different thermal energy storage technologies are available, including sensible, latent, and sorption and chemical reactions (also called thermochemical) energy storage. Although in the past twenty years, the scientific literature showed an increasing trend in the research of thermal energy storage integrated to the building sector, it was only in recent years that this concept was extended to the built environment, which includes residential and non-residential buildings, districts, and urban networks. This paper provides a comprehensive review and classification of thermal energy storage technologies applied in the built environment considering the trends and the future perspective of the past and current research. This work was partially funded by the Ministerio de Ciencia, Innovación y Universidades de España (RTI2018-093849-B-C31 - MCIU/AEI/FEDER, UE) and by the Ministerio de Ciencia, Innovación y Universidades - Agencia Estatal de Investigación (AEI) (RED2018-102431-T). The authors would like to thank the Catalan Government for the quality accreditation given to their research group GREiA (2017 SGR 1537). GREiA is a certified agent TECNIO in the category of technology developers from the Government of Catalonia. This work is partially supported by ICREA under the ICREA Academia programme.