An application of latent heat thermal energy storage systems with phase change materials seems to be unavoidable in the present world. The latent heat thermal energy storage systems allow for storing excessive heat during low demand and then releasing it during peak demand. However, a phase change material is only one of the components of a latent heat thermal energy storage system. The second part of the latent heat thermal energy storage is a heat exchanger that allows heat transfer between a heat transfer fluid and a phase change material. Thus, the main aim of this review paper is to present and systematize knowledge about the heat exchangers used in the latent heat thermal energy storage systems. Furthermore, the operating parameters influencing the phase change time of phase change materials in the heat exchangers, and the possibilities of accelerating the phase change are discussed. Based on the literature reviewed, it is found that the phase change time of phase change materials in the heat exchangers can be reduced by changing the geometrical parameters of heat exchangers or by using fins, metal foams, heat pipes, and multiple phase change materials. To decrease the phase change material’s phase change time in the tubular heat exchangers it is recommended to increase the number of tubes keeping the phase change material’s mass constant. In the case of tanks filled with spherical phase change material’s capsules, the capsules’ diameter should be reduced to shorten the phase change time. However, it is found that some changes in the constructions of heat exchangers reduce the melting time of the phase change materials, but they increase the solidification time.