Research on object deformation is always the hot point in the area of computer graphics and computer aided design. Free form deformation, which is one of the important technologies of object deformation, has been introduced into the popular modeling software and animation software successfully. In this paper, the research on free form deformation in the past twenty years has been conducted as a comprehensive survey. Firstly, the authors classify the existing technologies into accurate free form deformation and non accurate free form deformation, and then from the deformation tools used in the different methods, the non accurate free form deformation is classified into four classes: volume based method, surface based methods, curve based methods and point based methods. Furthermore, they also compare the existing non accurate methods of free form deformation by listing their advantages and disadvantages from the view of convenience of deformation tools creation, efficiency of parameterization, interactivity for users, versatility and their application in popular modeling software. The intrinsic relations between them are also presented. Finally, their applications in several practical fields and their research directions in the future are introduced. This survey is not only valuable for the scientific researchers in this field but also valuable for the practical users of 3D modeling software and 3D animation software.