It is often claimed that the cheapest energy is the one you do not need to produce. Nevertheless, this claim is somewhat unsubstantiated. In this article, we try to shed some light on this issue by using the energy return on investment (EROI) as a yardstick. This choice brings semantic issues because the EROI is used in a different context than that of energy production. Indeed, while watt and negawatt share the same physical unit, they are not the same object, which brings some ambiguities in the interpretation of EROI. These are cleared by a refined definition of EROI and an adapted nomenclature. This review studied the research in the energy efficiency of building operation, which is one of the most investigated topics in energy efficiency. Impact of insulation, high efficiency windows, and other energy efficiency measures were considered. These results were normalized for climate, life time of the building, and construction material. In many cases, energy efficiency measures imply a very high EROI. Nevertheless, in some circumstances, this is not the case and it might be more profitable to produce the required energy than trying to save it.