In this talk I will present some of the works developed with the aim to obtain a relevant mathematical model for (mainly) the bedload sediment transport. This problem is classically approximated by the Saint-Venant-Exner system but it has some drawbacks: the mass conservation is not ensured, the gravitational effects are not originally included and the system does not have an associated energy balance. In the first part I will show how we obtained a Saint-Venant-Exner type model from a formal asymptotic derivation that resolves these inconveniences. In a second work the bedload problem is tackled with a ``classical'' bilayer shallow model that serves to any flow regime, weak or strong, with the particularity of converging to the previous SVE problem for the slow regime. This model presents also an advantage from a numerical point of view since the gravitational effects are naturally included in the system. These works have been developed in collaboration with E. Fernández-Nieto, T. Morales and C. Escalante.