Machine learning (ML) has revolutionized medical image-based diagnostics. In this review, we cover a rapidly emerging field that can be potentially significantly impacted by MLeye tracking in medical imaging. The review investigates the clinical, algorithmic, and hardware properties of the existing studies. In particular, it evaluates 1) the type of eye-tracking equipment used and how the equipment aligns with study aims; 2) the software required to record and process eye-tracking data, which often requires user interface development, and controller command and voice recording; 3) the ML methodology utilized depending on the anatomy of interest, gaze data representation, and target clinical application. The review concludes with a summary of recommendations for future studies, and confirms that the inclusion of gaze data broadens the ML applicability in medical imaging from computer-aided diagnosis (CAD) to gaze-based image annotation, physicians' error detection, fatigue recognition, and other areas of potentially high research and clinical impact.