Fractured porous media are geometrically very complex. There are many competing model concepts to represent their structure in flow simulations; these models differ drastically in their level of geo¬metric detail and in their level of simplification and abstraction. Systematically choosing between these vastly different models, calibrating chosen models and specifying their predictive uncertainty is far from trivial. The goal of this project is to tackle the interlocked model-selection-and-calibration problem. Achieving this goal requires a list of algorithmic developments in the field of simulation-based Bayesian statistics.