  Quantifying the propagation of landslides is a key step for analyzing
gravitational risks. In this context, thin-layer models have met a growing
success over the past years to simulate the dynamics of gravitational flows,
such as debris flows. They are easier to use and require less computing
ressources than 3D models, and provide more detailed estimations of flow
thicknesses and velocities than purely empirical methods. In this literature
review, we present the main rheologies used to model homogeneous gravitational
flows, and describe a practical case study with debris flow modeling in the
Pr{\^e}cheur River (Martinique, Lesser Antilles). Then, we discuss possible
developments for operational hazard and risk assessment with thin-layer models.

Geophysics;Fluid Dynamics