In the literature on Explainable Artificial Intelligence (XAI), it is often claimed that explainability can ensure the fairness of AI-based decision-making [5, 25, 37]. However, fairness of AI-based decision-making is a complex and multi-dimensional issue, ranging from attempts at statistical definitions of fairness [11] via legal definitions of discrimination [4] to psychological research into perceived fairness [55]. Given this complexity, it is not always clear how explainability can help improve the fairness of AI decision-making. This paper reviews the concepts and approaches to fairness in AI decision-making in philosophy, psychology, law, and computer science and discusses the potential relationship with explainability. It suggests three ways in which explanations might be relevant for fairness: Explanations could be a conceptual requirement of fairness, a (potential) direct cause of fairness, or they could remove a barrier that hinders the use of other means to increase fairness. With the help of these three categories the paper clarifies how explainability might be used to improve the fairness of AI decision-making.