The emergence of Peer-to-Peer, Collective or Community Self-Consumption, and Transactive Energy concepts gives rise to new configurations of business models for local energy trading among a variety of actors. While much attention is paid in the academic literature to the transition of the underlying energy system with its macroeconomic market framework, fewer contributions focus on the microeconomic aspects of the broad set of involved actors. Even though specific case studies highlight single business models, a comprehensive analysis of emerging business models for the entire set of actors is missing. Following this research gap, the presented paper conducts a systematic literature review of 135 peer-reviewed journal articles to examine business models of actors operating in these energy markets. From 221 businesses in the reviewed literature, nine macro-actor categories are identified. For each type of market actor, a business model archetype is determined and characterized using the business model canvas framework. The key elements of each business model archetype are discussed, and areas are highlighted where further research is needed. Finally, this paper outlines the differences of business models for their presence in the three local energy market models. With a particular focus on the identified customers and partner relationships, the study highlights the key actors per market model and the character of the interactions between market participants.