This chapter provides an overview of the historical development and applications of Material Point Method. The material point method (MPM) is one amongst a vast number of computational methods being developed to simulate soil-water-structure interaction problems in history-dependent materials involving large deformations. MPM combines the advantages of mesh-based and point-based approaches: mesh distortion can be eliminated and history is stored in material points (MPs). MPM is an advanced formulation of the finite element method (FEM) where the continuum body is represented by a set of Lagrangian points, called MPs. The governing equations of the one-phase single-point formulation are general and not exclusive to geomechanical problems. The continuum satisfies the fundamental conservation laws of thermodynamics. These are the conservation of mass, the conservation of momentum and the conservation of energy. The basis of the two-phase double-point formulation follows from mixture theory extended by the concept of volume fractions to model the interaction between solid and liquid phases.