Fluid flow in porous materials are very common: examples range from groundwater flow and hydrogen storage in underground rocks to water discharge in fuel cells. Predictive numerical models of such flows are crucial tools to design such applications. These models however commonly fall short, because they fail to capture the effects of the puzzling underlying microscopic dynamics, namely: the flow physics that take place in the pores. The physics of these fluctuating, microscopic flows are poorly understood because it has proven very challenging to measure them in the 3D labyrinths formed by pore geometries. This is because measurements are severely hampered by the optical opacity of the materials, the high resolution that is needed, and the 3D nature of the processes. The FLOWSCOPY project aims to cause a paradigm shift by resolving this inaccessibility, enabling the measurement of unsteady 3D flows inside opaque porous materials. Its first goal is to enable the inspection of flow fields in all their µm-scale complexity, by creating a method that tracks tracer particles flowing through the pores with 3D X-ray imaging. To achieve the required millisecond imaging times - up to 3 orders of magnitude faster than the state-of-the-art – the new approach will retrieve tracer locations in each of the many radiographs that conventionally make up a single tomographic time frame. Then, FLOWSCOPY aims to untangle the upscaling problem, building the first method that can measure flow maps averaged on a sliding scale from nano- to centimetres. Finally, the newly developed methods’ transformative capabilities will be applied to two pertinent problems in arguably some of the most complex porous media: geological materials. First, FLOWSCOPY will investigate how two fluids, such as water and hydrogen gas, displace each other in porous rocks, aiming to explain capillary fluctuations that deviate from current models. Second, it aims to unriddle flows of viscoelastic fluids, such as those used to clean up polluted sediments, which exhibit a poorly understood transition from steady to chaotic dynamics. The focus will be on flows in geological materials, due to their relevance for the 21st century’s water and energy challenges and the difficulties induced by their complex pore structures. Beyond this, the new techniques will be applicable to a wide range of natural and engineered microstructures, from arteries to building materials.