Incoherent hopping conduction has been revealed as the electronic transport mechanism in lightly doped microcrystalline semiconductors at low temperatures. Although microcrystalline materials should be considered as geometrically inhomogeneous systems, essential features of the photoconductivity and dark conductivity in such systems can be successfully described by theoretical models based on a homogeneous distribution of localized states. We review several theoretical approaches suggested so far for the description of hopping transport in disordered materials. In order to verify the validity or analytical approaches. we have performed a series of straightforward computer simulations for the percolation problem in hopping conduction, The simulation results support the analytical approaches based on the transport energy concept and on percolation arguments for the description of the dark conductivity at low temperatures. (C) 2005 Elsevier B.V. All rights reserved.