Geomagnetic disturbances cause perturbations in the Earth's magnetic field which, by the principle of electromagnetic induction, in turn cause electric currents to flow in the Earth. These geomagnetically induced currents (GICs) also enter man-made technological conductors that are grounded; notably, telegraph systems, submarine cables and pipelines, and, perhaps most significantly, electric power grids, where transformer groundings at power grid substations serve as entry points for GICs. The strength of the GICs that flow through a transformer depends on multiple factors, including the spatiotemporal signature of the geomagnetic disturbance, the geometry and specifications of the power grid, and the electrical conductivity structure of the Earth's subsurface. Strong GICs are hazardous to power grids and other infrastructure; for example, they can severely damage transformers and thereby cause extensive blackouts. Extreme space weather is therefore hazardous to man-made technologies. The phenomena of extreme geomagnetic disturbances, including storms and substorms, and their effects on human activity are commonly referred to as geomagnetic hazards. Here, we provide a review of relevant GIC studies from around the world and describe their common and unique features, while focusing especially on the effects that the Earth's electrical conductivity has on the GICs flowing in the electric power grids.