Electrification is potentially the most efficient method of decarbonization of space, water, and in certain instances, process heating through the deployment of electrically driven heat pumps. However, challenges are noted in terms of electricity network capacity that ultimately must influence a holistic approach to building/process heating demand reductions which in turn must influence heat pump development, heat pump operations, heat pump capital cost, and the role of thermal storage. Approaches to these challenges are presented from a global and, a UK and Ireland perspective, as for the UK and Ireland, it is often muted that the electricity network is less well suited to addressing the electrification of heating. Thus, this work will consider the likely cost‐effective heat demand reductions in buildings and processes, how might heat pumps operate in future electricity markets and systems, how can we make heat pumps cheaper to purchase and cheaper to operate and what is the role and type of energy storage in terms of demand side management. Thermal energy storage will be considered for space heating (30°C–80°C), water heating (60°C+ to negate legionella), and lower temperature industrial process (up to e.g., 300°C). Furthermore, an analysis of a UK housing development is presented as a retrofit case study for social housing, illustrating the impacts of the electricity network, and approaches that can be taken, for example, thermal storage, to minimize such impacts. Higher temperature systems will be considered for process applications.