This paper provides a comprehensive review of distribution system state estimation in terms of basic definition, different methods, and their application. In the last few years, the operation of distribution networks has been influenced by the installation of distributed generations. In order to control and manage an active distribution network’s performance, distribution system state estimation methods are introduced. A transmission system state estimation cannot be used directly in distribution networks since transmission and distribution networks are different due to topology configuration, the number of buses, line parameters, and the number of measurement instruments. So, the proper state estimation algorithms should be proposed according to the main distribution network features. Accuracy, computational efficiency, and practical implications should be considered in the designing of distribution state estimation techniques since technical issues and wrong decisions could emerge in the control center by inaccurate distribution state estimation results. In this study, conventional techniques are reviewed and compared with data-driven methods in order to highlight the pros and cons of different techniques. Furthermore, the integrated distribution state estimation methods are compared with the distributed approaches, and the different criteria, including the level of area overlapping execution time and computing architecture, are elaborated. Moreover, mathematical problem formulation and different measuring methods are discussed.