Abstract Hopefully, it is now clear that stochastic algorithms are much more than a simple game of heads or tails for predicting what happens in the inter-well volume: various geological constraints can be incorporated with great flexibility. The compatibility of geostatistical representations with seismic or well tests data can also be controlled, which allows the integration of dynamic, acoustic and geological information in favourable cases. Differentiation about supposedly “deterministic” models that would be geologically right, and “random” models that would be geologically meaningless, is not relevant anymore: with stochastic models, what is known is treated as deterministic, and does not change between realisations, whilst what is not known is regarded as random and varies between realisations. Geostatistics is a powerful formalism, but it must be applied with care. More developments are needed before this discipline is fully accepted and used routinely. We believe that, in the future, the following developments will take place. A great variety of stochastic approaches are now available for distributing heterogeneities in space. These approaches will generate realistic models only if the reservoir geologist is involved early in the choice of the approach and of the statistical parameters to use. If geologists make the effort of understanding the philosophy of stochastic models, and if geostatisticians make their techniques easier to understand to non-specialists, more of the geologists’ experience will be accounted for and quantified, leading to more realistic stochastic models. As geologists become more aware of these techniques, the geology will drive the modelling algorithms rather than the opposite.