In the last decades, numerous stochastic methods have been developed and applied to deal with geological heterogeneity and uncertainty in groundwater modelling. Many studies have been published indicating the incorporating realistic geological heterogeneity and parameter and conceptual uncertainty can improve groundwater flow and solute transport simulations and decrease prediction uncertainty. Applying such methods on real world cases can however be challenging. These challenges might be the reason why such stochastic techniques have been used to a much lesser extent by practitioners than by researchers. This keynote lecture will give an overview of the current challenges and discusses new advancements to overcome them. An overview will be given of previous studies focusing on incorporating geological uncertainty through multiple-point geostatistics and on dealing with uncertainty using Bayesian approaches. The following questions will be discussed: How to build and select alternative hydrogeological conceptual models or 3D training images? Is it worth incorporating fine scale geological heterogeneity in groundwater problems or are other features (boundary conditions, data uncertainty/quality, …) more important for improving predictions? How can stochastic methods such multiple-point geostatistics and Bayesian uncertainty assessment methods be used without suffering from very long computation times for the numerical models? Is overparametrization of groundwater models an issue in this context? What are the practical obstacles to apply stochastic methods for dealing with geological heterogeneity and uncertainty by groundwater practitioners? This talk will also summarize the lessons learnt and present recommendations for future research and for application of stochastic methods in non-academic environments for practical real-world applications.