Interstellar ices are chemically processed by ultraviolet (UV) radiation to form complex products, and models of UV photochemistry provide powerful tools for the interpretation of astronomical observations. We have performed UV photolysis experiments on pure 10 K samples of nine ices of molecules of astrophysical interest: H2O, NH3, CH4, CO, CO2, O2, N2, H2CO, and CH3OH. Destruction of these species by photochemical processes is discussed, and the cross-sections for destruction are estimated for use in chemical models. New molecules produced during photolysis are identified on the basis of their characteristic infrared features, and their chemical origins and astrophysical implications are discussed. Rates of formation are also estimated for first-order products. In experiments with CH4 and with H2CO, molecules with as many as 7 - 8 C atoms are produced. Such results may indicate how and why very complex organic molecules are formed in molecular mixtures characteristic of interstellar ice mantles.