Explainable artificial intelligence (XAI) is gaining importance in physiological research, where artificial intelligence is now used as an analytical and predictive tool for many medical research questions. The primary goal of XAI is to make AI models understandable for human decision-makers. This can be achieved in particular through providing inherently interpretable AI methods or by making opaque models and their outputs transparent using post hoc explanations. This review introduces XAI core topics and provides a selective overview of current XAI methods in physiology. It further illustrates solved and discusses open challenges in XAI research using existing practical examples from the medical field. The article gives an outlook on two possible future prospects: (1) using XAI methods to provide trustworthy AI for integrative physiological research and (2) integrating physiological expertise about human explanation into XAI method development for useful and beneficial human-AI partnerships.