The role of interface between molecular material and electrode on currents and photocurrents is considered. Mechanisms of charge carrier injection, electrode recombination and transport are discussed. Particularly thermal, excitonic, photo and tunneling injection of charge carriers, diffusion in presence of image force, interface barrier between electrode and organic materials and two organic materials, non-uniformity of electrodes and other phenomena on charge carrier injection are considered. The data presented in the review which complete theoretical considerations have been taken from previous as well as current literature. The considered phenomena are very important for the analysis of many practical problems for molecular electronic devices such as rectification of current, organic transistors, electroluminescence, photovoltaic effects and some similar problems.