Digital signal processors (DSPs) are essential in power electronics and motor drives for industrial applications and academic research. The integration of machine learning (ML) into DSPs for these applications presents challenges such as limited data availability and the need for high-speed execution. Despite these difficulties, the researchers have developed successful strategies for incorporating ML into DSP frameworks. This work provides a comprehensive overview of integrating ML algorithms with DSPs in power electronics and motor drives, highlighting key strategies and addressing the challenges and innovations involved in optimizing these algorithms for practical use. A number of ML algorithms suitable for DSP implementation are also reviewed, with particular attention to a neural network-based surrogate model. Additionally, the review emphasizes real-time applications, such as fault detection, sensorless operation, and control, aiming to guide researchers on the effective implementation of ML in DSPs and encouraging the broader adoption of these integrated approaches across the industry.