The need of models for heterogeneous reservoirs has stimulated, for the last 15 years, the development of stochastic models, for instance pixel-based (indicator or truncated Gaussian simulations) or object-based (e.g. Boolean). Such models are flexible, some are easy to condition, however the geometry and arrangement of sedimentary bodies often lack realism when the geological context is better known. Multipoint statistics, for instance, are looking to improve the situation. Yet another generation of models, both process-based and stochastic, is able to provide satisfactory modelling for heterogeneous reservoirs by reproducing the depositional processes. This is illustrated in the case of reservoirs associated to meandering fluvial systems. The model consists of: 1) a channel evolving through time either continuously (according to hydraulics equations) or discontinuously (by avulsion); 2) the consistent deposition of the different sedimentary bodies (point-bars, crevasse splays, overbank alluvium…). In order to be operational, the model depends on a limited number of parameters and is computationally quick, while being able to produce a variety of architectures. Multirealizations are available thanks to the stochastic nature of parameters. The parameters can be inferred from data (e.g. through spatial statistics such as vertical proportion curves of facies). The model can be regionally constrained (e.g. to seismic), and it allows for some conditioning to well data.