Thermostatically controlled load (TCL) contributes a relatively higher proportion of energy consumption. Its mathematical models can be used for quantifying the real-time supply and demand balance between the power generations and load systems. The relevant studies have received great attention with the development of smart grids in recent years. This study mainly presented the development of TCL mathematical models from a single model to aggregated models. Finally, the advantages of these models were compared and analyzed based on the simulation results. This study could provide a theoretical basis for the applications of TCLs in the supply and demand balances.