Soft body impacts, namely hail or birds, are a serious and inevitable threat for the integrity of aircrafts, automobiles and trains windshield, wind towers nacelles, photovoltaic panels, amongst others. The development of impact resistant structures and the necessary experimental tests for validation are expensive, time consuming and complex, especially in aeronautics. Numerical simulation makes possible to reduce the overall development and testing costs by supporting the design stage and complementing testing campaigns. Numerical simulation relies on material and interaction models development and software to provide such supporting aid. Soft body models rely on explicit modelling of the microstructure, subjected to large deformation and separation, where mesh-free particle methods are most appropriate. This reviewing study focuses on mesh and mesh-free simulation models and methods, namely, Eulerian, Lagrangian, Arbitrary Lagrangian Eulerian (ALE), Coupled Eulerian-Lagrangian (CEL), Smoothed Particle Hydrodynamics, Particle Finite Element Method, and Discrete Element Method, and reviews approaches for soft bodies modelling through these methods. Applicability of each method as well as advantages and drawbacks will be discussed from the viewpoint of hail and bird impact phenomena.