This publication is devoted to creation of energy-efficient systems for cold supply and heat supply using heat energy accumulators. Thermal energy accumulation increases the efficiency of heat power systems including cooling and air conditioning systems, reduces peak power consumption and capacities of thermal installations at variable loads. It is shown that substances with phase transition (SPT) are widely used for thermal energy accumulation. They are mainly of the solid body-liquid type providing volume and mass density of heat storing and cold energy that is 5–14 times higher in comparison with accumulating liquids. Requirements to SPT with regard to thermal energy accumulators are formulated. We have given an overview of the SPT recommended for application to which organic compounds belong (paraffins, fatty acids), hydrates of salts, eutectics (may include organic and inorganic compounds in their structure). The advantages and disadvantages of each group of substances are shown. The information on the properties of certain SPT in relation to air conditioning systems is presented. It is shown that SPT having industrial applications are hidden under trademarks. It is noted that the creation of heat energy accumulation systems made in Russia requires carrying out a fundamental and applied research complex. We have presented application examples of thermal energy accumulation using SPT in air conditioning systems. The designs of thermal energy accumulators are described, their advantages and disadvantages are noted. We have carried out the analysis of calculation methods for systems with thermal energy accumulators available in literature including solutions of Stefan problem about non-stationary heat exchange at phase transitions in relation to the thermal energy accumulation. The conclusion is drawn on the numerical method advantages for solution of this problem. The research directions are formulated which implementation will allow for developing Russian systems of heat and cold supply with heat energy storage devices.