Electric (mechanical vapour-compression) heat pumps are acknowledged as a key technology for heat decarbonisation, their role being evidently more significant than thermally driven heat pumps and hydrogen boilers. The International Energy Agency estimates that, assuming governments meet their commitments, the global capacity of electric heat pumps will nearly triple by 2030. Heat pump systems come in a variety of designs, including system configurations, component (e.g., heat exchanger, compressor, working fluid) selection, and operation strategies that have a significant effect on performance and cost. In this article, we review current progress in technology development and in the methods used for techno-economic performance assessments of domestic (i.e., residential) heat pumps in the range of a few ∼kWs. The principles upon which heat pump operation and performance depend are first stated. Then, drawing from widely used performance indicators and published data on hundreds of commercially available heat pump products and components over a wide range of operating conditions, a detailed methodology is presented for obtaining performance and cost estimates. A synopsis of potential synergies with other heating, cooling and storage technologies is presented, demonstrating that appropriate integration and operation are required to maximise cost-effectiveness and emission reduction capabilities. Furthermore, whole-energy system implications of widespread heat electrification and current policy measures supporting electric heat pumps in different countries are discussed. The models and analyses presented in this review are useful to a diverse set of stakeholders, including energy technology and system modellers, technology manufacturers, end-users, government, and policy makers.