Cell migration is a fundamental process involved in many physiological and pathological processes such as the immune response and tumor metastasis. As a consequence, the ability of cells to ensure these functions is closely related to their long time migration behaviour. For cells crawling on a flat adhesive substrate, observed trajectories show a great diversity, ranging from brownian-like to very directional. This results from the complexity of the self-organized internal activity, involving physical and chemical interactions on several time and space scales. Understanding the long time cell behaviour is therefore challenging. In this talk, I will introduce a stochastic particle model for cell trajectories based on the observable cell dynamics. The model writes as a stochastic birth and death process for the dynamics of membrane deformations. Several scalings lead to either deterministic or stochastic models, that allow to characterize the diversity and efficiency of trajectories. Finally, I will discuss how the model con be confronted to experimental data, and how it can be enriched to take into account the interaction of cells with their environment.