Condition monitoring (CM) of power semiconductor devices enhances converter reliability and customer service. Many studies have investigated the semiconductor devices failure modes, the sensor technologies, and the signal processing techniques to optimize the CM. Furthermore, the improvement of power devices’ CM thanks to the use of the Internet of Things and artificial intelligence technologies is rising in smart grids, transportation electrification, and so on. These technologies will be widespread in the future, where more and more smart techniques and smart sensors will enable a better estimation of the state of the health (SOH) of the devices. Considering the increasing use of power converters, CM is essential as the analysis of the data obtained from multiple sensors enables the prediction of the SOH, which, in turn, enables to properly schedule the maintenance, i.e., accounting for the trade-off between the maintenance cost and the cost and issues due to the device failure. From this perspective, this review paper summarizes past developments and recent advances of the various methods with the aim of describing the current state-of-the-art in CM research.