Medical imaging is a cornerstone of modern healthcare, enabling precise diagnosis, treatment planning, and disease monitoring. Traditional machine learning (ML) approaches have significantly improved medical image analysis, yet they face challenges such as data scarcity, lack of interpretability, and variability in imaging protocols. Physics-Informed Machine Learning (PIML) offers a transformative solution by integrating fundamental physical laws, usually in partial differential equations and boundary conditions, into data-driven ML models. PIML constrains the solution space, enhances interpretability, and reduces the dependency on large, annotated datasets. This review provides an overview of the principles, methodologies, and applications of PIML in medical imaging, with a focus on imaging modalities such as MRI, CT, and ultrasound. We discuss the taxonomy of PIML approaches based on observational, inductive, and learning biases, showing their roles in enhancing model accuracy and generalization. Additionally, we explore the impact of PIML on image reconstruction, segmentation, enhancement, and anomaly detection, demonstrating its effectiveness in addressing noise, resolution, and diagnostic accuracy challenges. Despite its advantages, PIML faces challenges in the accurate representation of complex physiological processes, computational efficiency, and the integration of physics-based priors across diverse applications. This review points out future research directions including the development of hybrid models that combine PIML with deep learning techniques and large foundation models, improved benchmark datasets, and scalable algorithms for real-time applications. The findings of this review highlight PIML as a pivotal approach for advancing medical imaging, bridging the gap between theoretical models and practical implementation in clinical settings.