As high-quality single-crystal materials used in electronic devices approach the microscale and nanoscale, charge-transport phenomena in these devices result in inhomogeneous spatial signatures with strong implications for observable material properties. These signatures include spatially varying dissipation, which affects thermal management strategies in devices, and interface resistance between different materials, and are essential for the functional control of devices. In this Review, we investigate the spatially inhomogeneous signatures of charge flow in conductors, with particular emphasis on the recently rekindled field of electron hydrodynamics, a regime where electrons are strongly interacting and can flow collectively akin to fluids. We highlight recent experimental advances in transport measurements that enabled the observation of these signatures and review the theoretical frameworks used to interpret and predict these observations. We outline the new charge-transport phenomena introduced by crystal symmetry in materials, provide an outlook on future research opportunities and identify experimental and theoretical challenges in the study of hydrodynamic transport in materials.