The paper reviews our recent attempts at modelling bed load transport in mountain rivers. This is a longstanding issue that has attracted considerable attention over the last century. While a number of field and laboratory studies have been instrumental in getting the big picture, there is a clear lack of efficient methods for predicting bed evolution and particle flux. Most approaches to bed load transport have emphasized the existence of a oneto-one relationship between the particle flux and water discharge, but this result conflicts with the spread of data, which often spans over several orders of magnitude. A possible interpretation lies in the significance of the fluctuations of the particle flux together with the propagation of bed forms. We have therefore developed a theoretical model based on birth-death Markov processes to describe the random exchanges between the stream and bed, which then allows us to derive a governing equation for the particle flux fluctuations. We end up with the probability distribution function of the sediment transport rate. A striking feature is the existence of large fluctuations even under steady flow conditions. Numerical simulations have been carried out to compute the flow features, for the moment with no sediment transport. These simulations have shown that the kinematic wave approximation (which leads to a significant simplification of the Saint-Venant equation into a nonlinear advection equation) performs well for a wide range of water discharges. Remarkably, it has been found that under steady flow conditions, the local flow variables (wetted section and water discharge, or flow depth and mean velocity) exhibit a Froude similarity, i.e. regardless of the water discharge, the Froude number remains fairly constant at a given place of the river. Future work will consider the inclusion of a stochastic sediment transport equation in the Saint-Venant equations.