Abstract. We are going to introduce the concept of stochastic 3D modeling of geometrically complex (disordered) microstructures as a tool for virtual materials testing, including applications to battery electrodes as well as to electrodes of fuel cells, and solar cells. Using stochastic 3D models, one can generate a large variety of stochastically simulated micrsotructures with little computational effort. These virtual microstructures can be used as data basis to elucidate microstructure-property relationships. In this way, for example, effective conductivity can be expressed by microstructural characteristics such as volume fraction, tortuosity (windedness of transport paths) and costrictivity (bottleneck criterion) of the considered material phase. In another recent simulation study, we analysed more than 8000 virtual microstructures for various microstructural scenarios. Using data mining techniques like artificial neural networks and random forests, we were able to accurately predict effective conductivities given microstructure properties like volume fraction, tortuosity and constrictivity.