Abstract: The concept of medial axis was firstly put forward by Blum as an effective tool to describe 2Dshapes in image analysis, and it was subsequently generalized to represent geometric objects in higher dimensions,and applied in a wide range of areas such as shape discrimination, object retrieval, object segmentation,shape deformation and robots path planning, etc. In the last two decades, various methods havebeen proposed to extract medial axis. The purpose of the current paper is to make a comprehensive survey onthe related work, and to point out some future research problems.