Compressed-air energy storage is an attractive option for satisfying the increasing storage demands of electricity grids with high shares of renewable generation. It is a proven technology that can store multiple gigawatt hours of electricity for hours, days and even weeks at a competitive cost and efficiency. However, compressed–air energy storage plants need to be designed carefully to deliver these benefits. In this work, a consistent thermo-economic optimisation framework is applied to assess the performance and costs of different compressed–air energy storage configurations across different scales. Special attention is paid to the thermal energy stores, with both solid packed-bed stores and liquid stores examined as viable options for advanced compressed–air energy storage plants and different storage materials proposed for both options. The comprehensive thermo-economic optimisation, considering different system layouts, thermal energy storage technologies and storage materials, and system scales is a key novelty of the presented work. A configuration with two packed–bed thermal energy stores using Basalt as the storage material is found to perform best, achieving an energy capital cost of 140 $/kWh, a power capital cost of 970 $/kW and a roundtrip efficiency of 76% at a nominal discharge power of 50 MW and a charging / discharging duration of 6 h. The best-performing liquid storage material is solar salt, which is associated with an energy capital cost of 170 $/kWh and a power capital cost of 1,230 $/kW. Systems with liquid thermal energy stores however are found generally to perform worse than systems with packed–bed thermal energy stores both in terms of cost and efficiency across all scales.