This paper collects, summarizes, and discusses more than a hundred important works on various causes, approaches, and advances in the supervision and diagnosis of extruded power cables, particularly the diagnosis of partial discharge (PD) in XLPE cables. This review focuses on four aspects of research on the diagnosis of PD, namely the factors that affect PD in XLPE cables, comprehensive PD diagnosis under DC voltage, techniques for developing PD diagnosis, and lifetime analyses of XLPE cables. Several reviews on the diagnosis of PD in extruded power cables have been previously presented and analyzed. Nevertheless, most of the reviews tend to focus on the factors causing PD, and some discuss the diagnostic technique of PD in XLPE cable under AC voltage, while others do not provide a comprehensive review. In contrast with the previously published reviews, this paper highlights the factors that cause PD, PD diagnosis, and the remaining useful lifetime of XLPE cable under DC voltage. This review also provides the current position and development of PD diagnosis and lifetime XLPE cable under DC voltage, which can be a reference for further research for researchers regarding the actual impact of the topic in the field.