The incorporation of fairness into the distribution network (DN) planning and operation has become a key goal of recent studies. The cost of implementing fairness, denominated the price of fairness (PoF), covers the efficiency that is renounced for attaining social cohesion through fair outcomes. Locational disparity makes fairness schemes emerge to level the consumers playing field. However, fairness encompasses a range of notions. From egalitarian to merit-based criteria, various metrics are implemented as a tool for measuring equitable utility distribution. These have different mathematical complexities, from linear to non-linear programming cases, which affect their overall applicability. Hence, this study compiles the overarching fairness notions and metrics, reviewing how these affect stakeholders and the inherent mathematical optimisation in resource allocation problems. The aim is to support consistent and transparent planning and decision-making within DN operations.