Power quality is a pressing concern and of the utmost importance for advanced and high-tech equipment in particular, whose performance relies heavily on the supply’s quality. Power quality issues like voltage sags/swells, harmonics, interruptions, etc. are defined as any deviations in current, voltage, or frequency that result in end-use equipment damage or failure. Sensitive loads like medical equipment in hospitals and health clinics, schools, prisons, etc. malfunction for the outages and interruptions, thereby causing substantial economic losses. For enhancing power quality, custom power devices (CPDs) are recommended, among which the Dynamic Voltage Restorer (DVR) is considered as the best and cost-effective solution. DVR is a power electronic-based solution to mitigate and compensate voltage sags. This paper provides a thorough discussion and comprehensive review of DVR topologies based on operations, power converters, control methods, and applications. The review compares the state-of-the-art in works of literature, and comparative study on power quality issues, the DVR principle along with its operation modes, the DVR components, the DVR topologies based on energy storage, the DVR topologies based on single-/three-phase power converters, and the DVR topologies based on control units that have different control processing stages. Furthermore, modified and improved configurations of the DVR, as well as its integration with distributed generations, are described. This work serves as a comprehensive and useful reference for those who have an interest in researching DVRs.