SE, after it was first introduced to power systems by Fred Schweppes in 1970 [1], is nowadays an important function in the management and control of the operation of electric transmission networks all over the world. It has strengthened the SCADA systems and eventually led to the development of the EMS [2]. The state estimator obtains the system state using the SCADA measurements, measurements from PMUs [3,4], pseudo-measurements and the topology information [2,3]. After the state is known, various functions of EMS like contingency analysis, security analysis, optimal power flow and other functions can be carried out as shown in Fig. 1. Therefore, SE is the backbone function of TS EMS [5], however, its application to DS was not required. This was due to its passive nature with unidirectional power flows since there was no active generation at this level. However, due to shift towards the smart grid encompassing DG inputs and other features such as DR and DA functions, the shape of the power DS is changing and it is no longer passive due to bidirectional power flows (see, Fig. 2). This establishes a need for bringing DS into the operation circle of monitoring and control, which makes the role of DSSE more significant. DS and TS differ from one another in many ways, such as DS have high R/X ratios than TSs, imbalances among phases and low availability of real-time measurements. This makes the use of TSSE techniques unsuitable for application to DS. This paper is an attempt to encompass various SE techniques applied to DS by reviewing the relevant literature. Many review papers on the subject can be found with the deficiency of putting various techniques together but not mentioning the adequacy of those techniques for DS. This paper attempts to address this deficiency by mentioning the adequate estimation techniques for DS. It further provides future research directions for DSSE, including intelligent load modeling techniques [6] for pseudo measurement generation [7], event-triggered SE techniques [8], incorporation of smart meter [9] data and micro-synchrophasors (µPMU) [10] data in DSSE, and finally development of advanced energy management systems [6]. This paper is divided into the following sections: Section 2 presents SE and its mathematical formulation. Section 3 discusses the need for DSSE; modification on conventional SE for DSSE; NV- DSSE; BC-DSSE; and comparison of the voltage and branch current-based DSSE. Section 4 discusses the classification of DSSE techniques, Section 5 presents multi-area or distributed DSSE techniques, future research directions in DSSE, outlining five areas of active research on DSSE, are briefly discussed in Section 6, and finally Section 7 concludes the paper.