Cell migration is commonly involved in physiological and pathological phenomena. It is also a very complex process, since cell trajectories result from an intracellular self-organized activity spanning different space and time scales. In this talk, I will introduce a stochastic model for single cell trajectories based on a nonlinear measure-valued Markovian jump process for the membrane's deformation dynamics. Performing some scaling limit allows to obtain a nonlinear Stochastic Differential Equation for the cell velocity. Further analysis puts to light the ability of the model to capture several migratory behaviors and to derive key quantities of the dynamics. Finally, I will explain how this model can be enriched to take into account the cell's interaction with its environment.