Partial discharge (PD) detection and analysis plays a crucial role for acceptance testing and condition monitoring of power cables. Various aspects are related to PD in power cables from theory to practice. This paper first summarizes the PD mechanism and models used for PD analysis in power cables. Afterwards, PD detection is addressed in the aspects of off-line test, on-line test, and sensors. PD analysis is discussed in detail. Specifically, related quantities and algorithms for PD analysis are outlined. PD characteristics with affecting factors, e.g., dielectric type, load, and applied voltage are discussed. Experience on PD development trend with measurements in field is analyzed. Based on the comprehensive review, challenges of PD detection and analysis along a power cable are proposed.