Partial discharge (PD) signal detection is critical for maintaining the reliability of high voltage (HV) cable insulation systems, which are fundamental components of power transmission networks. Traditional PD detection methods, such as apparent charge measurement, electromagnetic emission detection, and acoustic detection, are widely used but have limitations, including sensitivity to noise, difficulty in localizing PD sources, and challenges in detecting incipient faults. This review emphasizes the role of rise time as a pivotal parameter in enhancing the precision of PD detection. By analyzing the rapidity of discharge events, rise time-based techniques offer improved diagnostic capabilities, enabling more accurate and timely identification of PD activities. This paper provides a comprehensive comparison of traditional and modern detection techniques, with a focus on rise time analysis, discussing their accuracy, applicability, and the experimental setups involved. Key findings from recent studies are highlighted, demonstrating the efficacy of rise time as a discriminator in PD signal analysis. The review concludes with recommendations for integrating rise time-based detection methods into existing monitoring frameworks and suggests future research directions to further refine these techniques. The insights gained underscore the importance of precise PD monitoring in extending the lifespan of HV cable systems and enhancing the reliability of power transmission infrastructures.