Heterogeneity is the single most salient feature of hydrogeology. Addressing heterogeneity in all its manifestations has been the focus of exciting and intense research over the last 50 years. Predictions of groundwater flow and transport processes and assessment of uncertainty are usually dealt with either deterministically through upscaling (spatial averaging) of the parameters or stochastically through the evaluation of relevant statistical moments of state variables. Stochastic models of groundwater flow and transport have progressed from models that had relatively limited use because of their unrealistically strong assumptions to recent models that allow realistic levels of material heterogeneity and formal assimilation of various types of information to provide predictions and associated bounds of uncertainty. Recent stochastic models suggested the manifestation of new processes arising at different scales. This is opening new avenues for the interpretation of observed processes, examples of which include the response of aquifers to imposed stresses and the way this can be related to the underlying heterogeneous structure of the medium as well as the clarification of the impact of heterogeneity on transport mechanisms across space-time. This session is aimed at providing an opportunity for specialists to exchange information and to introduce various existing and novel alternative stochastic models of subsurface flow and transport to the general hydrologic community. Focus is placed on recent key developments in theoretical aspects dealing with accurate and efficient quantification of uncertainty for flow and transport processes in the subsurface in the presence of multiple information and field/laboratory applications of stochastic models of groundwater flow and transport with special emphasis on methodological, conceptual and practical issues.