I will provide an overview of the current revolution in our understanding of flow, transport and reaction processes in porous media, enabled by 3D imaging from the nanometer scale upwards, micro-fluidics, and improved numerical methods. This will be illustrated by examples from work at Imperial College London on multiphase flow in rocks with application to carbon dioxide storage and oil recovery. X-rays are used to image flow processes in rocks at a spatial resolution of down to 1 micron and a time resolution between 1 and 1,000 s. These experiments can be used to measure traditional multiphase flow properties – relative permeability and capillary pressure – while providing pore-scale insight into displacement processes. We show how an accurate characterization of wettability, or the local distribution of contact angle, enables us to understand flow and trapping, and explain the circumstances which are optimal for storage or recovery applications. The experiments also provide a wealth of data to calibrate and validate pore-to-core scale flow and transport models.