System identification is fundamental in many recent state-of-the-art developments in power electronic such as modelling, parameter tracking, estimation, self-tuning and adaptive control, health monitoring, and fault detection. Therefore, this paper presents a comprehensive review of parametric, non-parametric, and dual hybrid system identification for DC-DC Switch Mode Power Converter (SMPC) applications. The paper outlines the key challenges inherent with system identification for power electronic applications; speed of estimation, computational complexity, estimation accuracy, tracking capability, and robustness to disturbances and time varying systems. Based on literature in the field, modern solutions to these challenges are discussed in detail. Furthermore, this paper reviews and discusses the various applications of system identification for SMPCs; including health monitoring and fault detection.