The constitutive model is the most important factor in the simulation of deformable solids. The stress-strain relationship of the existing basic constitutive models have some limitations and the deformation behaviors are relatively simple. In recent years, a quantity of researches have been placed on how to design more complex material models to satisfy the designers' requirements. In this paper, the material model is divided into three categories:the traditional homogeneous materials with same material parameters of the whole model, heterogeneous materials with composite structures, and the editing models of the material parameters and structures and the elastic behavior editing models based on the existing traditional constitutive models. Additionally, the current material design methods are reviewed, and recent researches, with their advantages and limitations, are analyzed. Finally, the current major challenges and future works are discussed.