Mechanical properties and constitutive models of solid propellants were reviewed from experimental techniques, mechanical parameters determination and developing constitutive models. Based on that, the current shortage and future research contents were also proposed. Firstly, up to now, experimental techniques of mechanical properties on solid propellants is still difficult under dynamic loading conditions and multiaxial stress conditions. Solving this problem can refer to the test methods for other strain-rate sensitive materials. Secondly, there is limited information available on the relationship of the mechanical parameters for solid propellants under different stress conditions. To solve this problem, it is necessary to refer to the research methods or means and basic conclusions of other nonmetal materials. Finally, there is a great gap between the practical need and the current studies on the constitutive models of solid propellants, especially the large deformation nonlinear viscoelastic constitutive models under dynamic loading conditions. The method of developing integral-type nonlinear viscoelastic constitutive models incorporating the damage on a macro-scale can be suggested to establish the constitutive models. However, the main emphasis is to derive and solve the damage function, which should be properly selected based on the deformation of solid propellants under dynamic loading conditions.