Interfaces between organic semiconductors and inorganic oxides provide the functionality for devices including field-effect transistors (FETs) and organic photovoltaics. Organic FETs are sensitive to the physical structure and electronic properties of the few molecular layers of material at the interface between the semiconducting channel and the gate dielectric, and provide quantitative information such as the field-effect mobility of charge carriers and the concentration of trapped charge. In this thesis, FET interfaces between organic small-molecule semiconductors and SiO2, and donor/acceptor interfaces between organic small-molecules and the wide bandgap semiconductor ZnO are studied using electrical measurements of field-effect transistor devices. Monolayer-scale films of dihexyl sexithiophene are shown to have higher hole mobility than other monolayer organic semiconductors, and the origin of the high mobility is discussed. Studies of the crystal structure of the monolayer using X-ray structural probes and atomic force microscopy reveal the crystal structure is different in the monolayer regime compared to thicker films and bulk crystals. Progress and remaining challenges are discussed for in situ X-ray diffraction studies of the dynamic changes in the local crystal structure in organic monolayers due to charge carriers generated during the application of electric fields from the gate electrode in working FETs. Studies were conducted of light sensitive organic/inorganic interfaces that are modified with organic molecules grafted to the surface of ZnO nanoparticles and thin films. These interfaces are models for donor/acceptor interfaces in photovoltaics. The process of exciton dissociation at the donor/acceptor interface was sensitive to the insulating or semiconducting molecules grafted to the ZnO, and the photoinduced charge transfer process is measured by the threshold voltage shift of FETs during illumination. Charge transfer between light sensitive donor molecules based on rhenium bipyridine complexes and ZnO thin films was measured using FETs, revealing the role of positive trapped charge in persistent photoconductivity in donor sensitized ZnO. The carboxylic acid attachment chemistry, used to anchor the donor molecules, is demonstrated to enhance the conductivity of ZnO thin films. The mechanism for the enhanced conductivity is linked to the passivation of defects on the surface of the ZnO.