In recent years, the rapid advances in Artificial Intelligence (AI) techniques along with an ever-increasing availability of healthcare data have made many novel analyses possible. Significant successes have been observed in a wide range of tasks such as next diagnosis prediction, AKI prediction, adverse event predictions including mortality and unexpected hospital re-admissions. However, there has been limited adoption and use in the clinical practice of these methods due to their black-box nature. A significant amount of research is currently focused on making such methods more interpretable or to make post-hoc explanations more accessible. However, most of this work is done at a very low level and as a result, may not have a direct impact at the point-of-care. This tutorial will provide an overview of the landscape of different approaches that have been developed for explainability in healthcare. Specifically, we will present the problem of explainability as it pertains to various personas involved in healthcare viz. data scientists, clinical researchers, and clinicians. We will chart out the requirements for such personas and present an overview of the different approaches that can address such needs. We will also walk-through several use-cases for such approaches. In this process, we will provide a brief introduction to explainability, charting its different dimensions as well as covering some relevant interpretability methods spanning such dimensions. We will touch upon some practical guides for explainability and provide a brief survey of open source tools such as the IBM AI Explainability 360 Open Source Toolkit.