One of the big concerns when planning the expansion of power distribution systems (PDS) is reliability. This is defined as the ability to continuously meet the load demand of consumers in terms of quantity and quality. In a scenario in which consumers increasingly demand high supply quality, including few interruptions and continuity, it becomes essential to consider reliability indices in models used to plan PDS. The inclusion of reliability in optimization models is a challenge, given the need to estimate failure rates for the network and devices. Such failure rates depend on the specific characteristics of a feeder. In this context, this paper discusses the main reliability indices, followed by a comprehensive survey of the methods and models used to solve the optimal expansion planning of PDS considering reliability criteria. Emphasis is also placed on comparing the main features and contributions of each article, aiming to provide a handy resource for researchers. The comparison includes the decision variables and reliability indices considered in each reviewed article, which can be used as a guide to applying the most suitable method according to the requisites of the system. In addition, each paper is classified according to the optimization method, objective type (single or multiobjective), and the number of stages. Finally, we discuss future research trends concerning the inclusion of reliability in PDS expansion planning
