Artificial Intelligence (AI) describes computer systems able to perform tasks that normally require human intelligence, such as visual perception, speech recognition, decision-making, and language translation. Examples of AI techniques are machine learning, neural networks, and deep learning. AI can be applied in many different areas, such as econometrics, biometry, e-commerce, and the automotive industry. In recent years, AI has found its way into healthcare as well, helping doctors make better decisions (“clinical decision support”), localizing tumors in magnetic resonance images, reading and analyzing reports written by radiologists and pathologists, and much more. However, AI has one big risk: it can be perceived as a “black box”, limiting trust in its reliability, which is a very big issue in an area in which a decision can mean life or death. As a result, the term Explainable Artificial Intelligence (XAI) has been gaining momentum. XAI tries to ensure that AI algorithms (and the resulting decisions) can be understood by humans. In this narrative review, we will have a look at some central concepts in XAI, describe several challenges around XAI in healthcare, and discuss whether it can really help healthcare to advance, for example, by increasing understanding and trust. Finally, alternatives to increase trust in AI are discussed, as well as future research possibilities in the area of XAI.