High-temperature thermal-energy storage has applications in concentrated solar power, advanced adiabatic compressed air energy storage, and industrial processes. Thermal-energy storage designs are often categorized according to the storage mode, that is, whether the thermal energy is stored in the form of sensible heat, latent heat, or thermochemical energy. Sensible-heat storage is the simplest, most mature, and hence most widely used storage mode. Latent heat and thermochemical energy storage offer the potential of higher storage densities, but have so far not seen widespread application. Because the advantages of one storage mode can often compensate for disadvantages of another storage mode, we have investigated combinations of storage modes such as combined sensible-latent or sensible-thermochemical storage, for example. In the presentation, we will show numerical and experimental results from our investigations of sensible, combined sensible-latent, and combined sensible-thermochemical storage. The results include experimental data from a pilot-scale plant for advanced adiabatic compressed air energy storage in the Swiss Alps. This pilot-scale plant used a combined sensible-latent thermal-energy storage unit placed directly in a hard-rock cavern.