Recently, much progress has been made on understanding transport properties of strongly coupled quantum field theories by employing gauge-gravity duality. However, a theory of transport at finite density and temperature is still lacking for strongly disordered systems. We reduce the computation of direct current electrical conductivity, for a wide variety of strongly disordered holographic systems with no background charge density, to the solution of a linear differential equation dependent only on data on the black hole horizon of the bulk theory. Some strongly coupled theories in two spatial dimensions have a universal conductivity, independent of disorder strength. We realize a disorder-driven holographic metal-insulator transitions through the percolation of poorly-conducting regions across the black hole horizon. We compare results from our exact realizations of holographic disorder with simpler approaches to the problem, such as massive gravity.