Deep learning methods have been very effective for a variety of medical diagnostic tasks and have even outperformed human experts on some of those. However, the black-box nature of the algorithms has restricted their clinical use. Recent explainability studies aim to show the features that influence the decision of a model the most. The majority of literature reviews of this area have focused on taxonomy, ethics, and the need for explanations. A review of the current applications of explainable deep learning for different medical imaging tasks is presented here. The various approaches, challenges for clinical deployment, and the areas requiring further research are discussed here from a practical standpoint of a deep learning researcher designing a system for the clinical end-users.