In recent years, natural hazards involving large mass movements such as landslides, debris flows, and mud flows have been increasing their frequency and intensity as a consequence of climate change and other related factors. These phenomena often carry huge rocks and heavy materials that may, directly or indirectly, cause damage to structures and the landscape. They are, therefore, extremely dangerous and often bring a huge loss of lives and properties, resulting in a great economic loss. While the Finite Element Method (FEM) represents a recognized, well established and widely used technique in many engineering fields, unfortunately it shows some limitation when dealing with problems where large deformation occurs. In the last decades many possible solutions and alternatives have been proposed and developed to overcome this drawback, among them one possibility is the use of the so called \emph{particle-based methods}. Among these, the Material Point Method (MPM) blends the advantages of both mesh-based and mesh-less methods. MPM avoids the problems of mesh tangling while preserving the accuracy of Lagrangian FEM and it is especially suited for non linear problems in solid mechanics and fluid dynamics. The talk will show some recent advances in MPM formulations, presenting both an irreducible and mixed formulation stabilized using variational multiscale techniques, as well as the partitioned coupling strategies with other techniques such as FEM or DEM. 2 a 3 dimensional validation examples have been performed to assess the current approaches. All algorithms are implemented within the Kratos-Multiphysics open-source framework and available under the BSD license.