Serious local insulation defects in power cables can cause distinct voltage and current disturbances. Precisely identifying these disturbances empowers utility companies to proactively manage cable maintenance and prevent unexpected power outages. This paper presents a comprehensive review of related research, detailing voltage and current disturbance waveforms across different systems. It categorizes existing incipient fault detection methods based on detection principles and data types, distinguishing between time-frequency characteristic threshold-based and artificial intelligence-based methods for transient power disturbances analysis. The study conducts a thorough comparison and evaluation of these methods. Drawing from existing research, recommendations are provided for further research on online detection technology for cable incipient faults.