It is now widely confirmed by scientific evidence that greenhouse gas emissions must be reduced to counteract the effects of global warming. The production of heat for industrial purposes is responsible for 36.8% of world energy-related emissions due to the widespread use of fossil fuels. Heat pumps are a key technology in the transition towards more sustainable industrial processes. In this paper, a systematic review of the literature produced in the last 5 years in international journals regarding the integration of heat pumps in industrial processes is presented. Firstly, papers presenting innovative configurations for high temperature heat pumps (HTHP), i.e., heat pumps delivering temperatures in the range between 100 °C and 200 °C, suitable for many industrial processes but still under development, are reviewed. Then, papers reporting innovative solutions for the integration of heat pumps in specific industrial processes and sectors (e.g., distillation, drying, desalination, etc.) are analyzed. Finally, the literature about alternative low-GWP refrigerants for industrial heat pumps, both pure compounds and mixtures, is described. It is concluded that many progresses have been realized in the last 5 years (2020–2024) regarding the identification of innovative heat pumps for industrial applications, but further research is certainly required.