Up to the present, the charge carrier transport properties of molecular organic materials are still extensively investigated. Since the introduction of triarylamines as hole transporting materials into xerographic systems, a wide range of different molecular materials systems have been investigated as hole and electron transporting materials. This paper discusses the theory of carrier conduction in both amorphous and crystalline organic materials. It also reviews th materials systems used as hole and electron transporters in organic light emitting diodes (LEDs), solar cells and transistors.