The rapidly increasing penetration of distributed energy resources (DERs) calls for a hierarchical framework where aggregating entities handle the energy management decisions of small DERs and represent these DERs upstream. These energy management decisions are typically envisaged to be made via market-based frameworks, aspiring the so-called Local Electricity Markets (LEMs). A rich literature of studies models such LEMs adopting various modeling assumptions and proposes various Market Mechanisms towards making dispatch and pricing decisions. In this paper, we make a systematic presentation of a LEM formulation, elaborating on the cornerstone attributes of the market model, i.e. the Market Scope, the Modeling Assumptions, the Market Objective, and the Market Mechanism. We discuss the different market model choices and their implications and then focus on the prevailing approaches of Market Mechanisms. Finally, we classify the relevant literature based on the market model that it adopts and the proposed Market Mechanism, visualize the results and also discuss patterns and trends.