This chapter offers a broad survey of the literature on mathematical explanation, and shows the importance of this area of work for a philosophical understanding of mathematical practice and for other philosophical areas such as metaphysics and epistemology. The discussion begins with a distinction between mathematical explanations of scientific facts and mathematical explanation of mathematical facts. The former topic leads naturally to a discussion of new versions of the indispensability argument and the latter to a discussion of the two major accounts of mathematical explanation available, e.g. those of Steiner and Kitcher.