Mudstones (shales) are of particular importance as the source rocks for oil and gas, and increasingly so as the reservoirs for unconventional hydrocarbons. They are also the most common sedimentary rocks on Earth, and, hence, are frequently encountered in excavations and foundations for buildings. These factors point to a pressing need to develop an increased fundamental understanding of their geomechanical and petrophysical properties. The mineral content of mudstones has a dominant effect on their mechanical properties. Presence of clay minerals within them results in plasticity and ductility that can pose particular engineering challenges, but swelling clays in particular can lead to serious problems of mechanical stability of boreholes and in construction. Good hydraulic fracture performance is linked to brittleness and high elastic moduli. This in turn is favoured by high silica or carbonate content and diagenetic cementation. Permeability to fluids depends on the interconnectivity of storage pores through orientated crack networks. New advances in imaging technologies are permitting very-high-resolution three-dimensional imaging down to the nanometre scale. Such studies will eventually lead to technological advances that exploit more effectively these enigmatic rocks.