Recent developments in Artificial Intelligence have increasingly focused on explainability research. The potential of Explainable Artificial Intelligence (XAI) in producing trustworthy computer-aided diagnosis systems and its usage for knowledge discovery are gaining interest in the medical imaging (MI) community to support the diagnostic process and the discovery of image biomarkers. Most of the existing XAI applications in MI are focused on interpreting the predictions made using deep neural networks, typically including attribution techniques with saliency map approaches and other feature visualization methods. However, these are often criticized for providing incorrect and incomplete representations of the black-box models’ behaviour. This highlights the importance of proposing models intentionally designed to be self-explanatory. In particular, part-prototype (PP) models are interpretable-by-design computer vision (CV) models that base their decision process on learning and identifying representative prototypical parts from input images, and they are gaining increasing interest and results in MI applications. However, the medical field has unique characteristics that could benefit from more advanced implementations of these types of architectures. This narrative review summarizes existing PP networks, their application in MI analysis, and current challenges.