The need to manufacture more competitive equipment, together with the emergence of the digital technologies from the so-called Industry 4.0, have changed many paradigms of the industrial sector. Presently, the trend has shifted to massively acquire operational data, which can be processed to extract really valuable information with the help of Machine Learning or Deep Learning techniques. As a result, classical Condition Monitoring methodologies, such as model- and signal-based ones are being overcome by data-driven approaches. Therefore, the current paper provides a review of these data-driven active supervision strategies implemented in electric drives for fault detection and diagnosis (FDD). Hence, first, an overview of the main FDD methods is presented. Then, some basic guidelines to implement the Machine Learning workflow on which most data-driven strategies are based, are explained. In addition, finally, the review of scientific articles related to the topic is provided, together with a discussion which tries to identify the main research gaps and opportunities.