Among the most dangerous natural phenomena for the safety of people, landslides are one of the most problematic: not only because of their potentially catastrophic consequences in terms of human and economic losses, but also because of their intrinsic unpredictability. Accurate numerical modeling of landslide dynamics therefore plays a crucial role in risk mitigation. In this work, we show some recent results on Material Point based schemes [NVB2023] for fluid flow applied to the simulation of the run-out phase of landslides. This phase, which follows the triggering event, includes the propagation of the material along the slope, its interaction with obstacles and, eventually, its deposition. The basic mathematical model used to describe gravity-driven free surface flows is based on the depth-integrated Navier-Stokes equation for an incompressible fluid [Fois2024]. From the numerical point of view the Material Point Method (MPM) can be interpreted as a semi-Lagrangian scheme where Lagrangian particles move on an underlying fixed FEM grid. The renewed interest in this class of methods is due to their amenability to parallel implementation also on GPU architectures. Numerical results are presented for both academic tests and realistic landslide scenarios, demonstrating the capability of the proposed approach to reproduce key features of landslide run-out dynamics. [Fois2024] M. Fois, C. de Falco, L. Formaggia, A Semi-conservative depth-averaged material point method for fast flow-like landslides and mudflows, Comm. in Nonlin. Science and Num. Simul., 2024. [NVB2023] V. P. Nguyen, A. de Vaucorbeil, S. Bordas, The Material Point Method Theory, Implementations and Applications, Springer, 2023.