This paper remedies the lack of comparison between studies specifically addressing partial discharge (PD) localization using electrical techniques. It identifies all the elements in need in each technique as well as the equations leading to a precise determination of the discharge site in a cable with a certain length and documents several circuit models set to simulate various types of PD. From the details in this paper, different detection methods can be combined based on the specific requirements of each method for detecting PD. This work thoroughly evaluates several electrical PD detection approaches, including time-based, frequency band, and electromagnetic time reversal (EMTR). Additionally, it gathers circuit modeling for various types of PD along cables to improve detection accuracy. It is evident that all time-dependent methods, despite their simplicity and requiring only a small number of components, face challenges when applied to long cables. This is primarily due to their reliance on signal propagation time. The authors provide profound insights into suggestions for future study areas. This review will provide essential insights and serve as a foundation for researchers to develop more effective methods for detecting PD in cables.