Energy storage systems are essential to secure a reliable electricity and heat supply in an energy system with high shares of fluctuating renewable energy sources. Thermal energy storage systems offer the possibility to store energy in the form of heat relatively simply and at low cost. In concentrating solar power systems, for instance, molten salt‐based thermal storage systems already enable a 24/7 electricity generation. The use of liquid metals as heat transfer fluids in thermal energy storage systems enables high heat transfer rates and a large operating temperature range (100°C to >700°C, depending on the liquid metal). Hence, different heat storage solutions have been proposed in the literature, which are summarized in this perspective. Based on these, future technical advances are suggested such as reducing the liquid metal share in the heat storage, using waste material as storage medium or using liquid metal as heat transfer fluids not only in sensible, but in latent or thermochemical energy storage systems. The use of waste material in a packed bed configuration with 5% porosity, for example, can bring down the storage material costs to 2%–3% of the costs of a liquid metal‐only storage system. Furthermore, future application fields beyond concentrating solar power are proposed: supply of industrial process heat, waste heat integration and power‐to‐heat‐to‐power processes.