The effects of climate change, in combination with the recent energy crisis, have brought the energy efficiency issues of hospitals markedly to the fore. Hospitals are considered among the most energy-intensive buildings, which is why they have become a top priority for governments wishing to upgrade their energy efficiency. Given the critical nature of the work of hospitals and the model of healthcare provision (nursing cover 24 h per day, 7 days a week) it is very hard to achieve energy cuts. The international literature shows that the energy efficiency of hospitals is a complex process that requires further research. This need is covered by the present systematic literature review, which captures the existing knowledge on energy monitoring strategies, assessment, and upgrading through technology, resources-saving strategies, and the relationship between energy efficiency and the quality of the service provision, while also identifying future research considerations and the potential for supporting researchers’ work. Additionally, this study adds aggregated data to the literature, as far as the energy performance of buildings is concerned, and allows investors to have data exported from energy surveys at their disposal. At the same time, it suggests the further exploration of alternative energy technologies, based on all renewable energy sources rather than only solar power systems. This highlights the need for a comparative examination of hospitals with different climatic and socio-economic environments, to better determine what technologies effectively serve the energy needs of each region. Finally, this survey considers it necessary to connect the energy efficiency of hospital units with the awareness of the management and workforce in the saving of energy resources. Due to the fact that most studies are oriented toward the energy performance of very large-sized hospitals, it is suggested that in the future, the research lens should also be focused on the smaller private and public sectors’ health units.