Eye-gaze tracking research offers significant promise in enhancing various healthcare-related tasks, above all in medical image analysis and interpretation. Eye tracking, a technology that monitors and records the movement of the eyes, provides valuable insights into human visual attention patterns. This technology can transform how healthcare professionals and medical specialists engage with and analyze diagnostic images, offering a more insightful and efficient approach to medical diagnostics. Hence, extracting meaningful features and insights from medical images by leveraging eye-gaze data improves our understanding of how radiologists and other medical experts monitor, interpret, and understand images for diagnostic purposes. Eye-tracking data, with intricate human visual attention patterns embedded, provides a bridge to integrating artificial intelligence (AI) development and human cognition. This integration allows novel methods to incorporate domain knowledge into machine learning (ML) and deep learning (DL) approaches to enhance their alignment with human-like perception and decision-making. Moreover, extensive collections of eye-tracking data have also enabled novel ML/DL methods to analyze human visual patterns, paving the way to a better understanding of human vision, attention, and cognition. This systematic review investigates eye-gaze tracking applications and methodologies for enhancing ML/DL algorithms for medical image analysis in depth.