The application of supervised Machine Learning (ML) in material science, especially towards the design of structural Multi-Principal Element Alloys (MPEAs) has rapidly accelerated over the past five years. However, several factors are limiting the impact that these ML methodologies can have, chief amongst them being the availability and fidelity of data. This review analyses how ML has been utilised to accelerate the design of novel structural MPEAs, outlining the standard procedures followed, and highlighting the successes and common pitfalls identified in current studies. The need for experimental validation and incorporation into closed loop ML pipelines is also discussed, including the influence and integration of manufacturing methodologies into the ML decision making process.