Advances in deep learning (DL) have transformed the analysis of medical images for conditions such as diabetic foot ulcers (DFU), breast cancer, and COVID-19. Although these models are highly accurate in their predictions, their limited transparency hinders their clinical use. Described artificial intelligence (XAI) methods, such as Grad-CAM, SHAP, and LIME, have been created to improve interpretability and foster greater trust in these models. This systematic review critically examines recent studies that combine deep learning and explainable AI to address three major healthcare challenges: detecting diabetic foot ulcers, breast cancer imaging, and COVID-19 diagnosis using various imaging techniques, including DFU images, mammography, computed tomography, and X-rays. These studies showcase a range of convolutional neural network (CNN) models, from lightweight, custom-designed models (such as LW-CORONet and COVID-XNet) to more advanced models, including ResNet, DenseNet, and Inception. Our findings suggest that interpretable models can achieve an accuracy above 95% while also providing clinicians with visual and quantitative insights. Challenges include limited dataset diversity, insufficient external validation, and the lack of standardized metrics for interpretability. Overcoming these issues is crucial for encouraging the use of AI tools in clinical practice. The review concludes with recommendations for future research that aims to improve the robustness of the model, integrate multimodal data, and improve clinical utility. These methods, including Grad-CAM, SHAP, and LIME, are crucial for enhancing the interpretability of deep learning models, enabling clinicians to understand how predictions are made. By increasing transparency and trust in AI systems, these techniques can ultimately improve patient outcomes and facilitate a smoother integration of technology in healthcare.