Medical image fusion, which aims to combine multi-source information captured by different imaging modalities, is of great significance to medical professionals for precise diagnosis and treatment. In the last decade, sparse representation (SR)-based approach has emerged as a very active direction in the field of medical image fusion, due to its powerful ability for image representation. In this paper, we mainly present an overview of the recent advances achieved in SR-based medical image fusion, ranging from the conventional local and single-component SR-based methods to the latest global and multi-component SR-based methods. In addition, several major challenges remained in this direction are presented and some future prospects are discussed.