Power systems are going through a transition period. Consumers want more active participation in electric system management, namely assuming the role of producers−consumers, prosumers in short. The prosumers’ energy production is heavily based on renewable energy sources, which, besides recognized environmental benefits, entails energy management challenges. For instance, energy consumption of appliances in a home can lead to misleading patterns. Another challenge is related to energy costs since inefficient systems or unbalanced energy control may represent economic loss to the prosumer. The so-called home energy management systems (HEMS) emerge as a solution. When well-designed HEMS allow prosumers to reach higher levels of energy management, this ensures optimal management of assets and appliances. This paper aims to present a comprehensive systematic review of the literature on optimization techniques recently used in the development of HEMS, also taking into account the key factors that can influence the development of HEMS at a technical and computational level. The systematic review covers the period 2018−2021. As a result of the review, the major developments in the field of HEMS in recent years are presented in an integrated manner. In addition, the techniques are divided into four broad categories: traditional techniques, model predictive control, heuristics and metaheuristics, and other techniques.