This survey reviews the recent development of mesh deformation methods. During the past two decades a vast number of researches have been concerned with developing an efficient and robust mesh deformation technique. This has been achieved either by proposing a novel approach, improving an existing one, or by combining two existing approaches together resulting in a new hybrid approach. It is important to keep track of the most up to date developments in the field of mesh deformation, in order to allow the researchers to adopt the most efficient and application compatible scheme as well as to propose new methods of improvements. In this survey the mesh deformation techniques have been classified into two main categories, 1) physical analogy based techniques and 2) interpolation based techniques. The most significant techniques under these two classes are reviewed and the aspects of strength and weaknesses are highlighted.