In this talk, I will present a family of landscape evolution model describing a surface eroded by a fluid. The main purpose is to understand the formation of patterns like rivers or canals with several branches and their time evolution. Then, I will focus on one particular model describing the evolution of a surface z, the fluid height h and the sediment concentration c in the fluid. I will present both a well-posedness result and a spectral stability analysis of some stationary states. Finally, I will present some numerical aspects of the problem and show several numerical simulations. This is a joint work with Julie Binard (Univ Sevilla) and Pierre Degond (IMT).