Of the over 150 different molecular species detected in the interstellar and circumstellar media, approximately 50 contain 6 or more atoms. These molecules, labeled complex by astronomers if not by chemists, all contain the element carbon and so can be called organic. In the interstellar medium, complex molecules are detected in the denser sources only. Although, with one exception, complex molecules have only been detected in the gas phase, there is strong evidence that they can be formed in ice mantles on interstellar grains. The nature of the gaseous complex species depends dramatically on the source where they are found: in cold, dense regions they tend to be unsaturated (hydrogen-poor) and exotic, whereas in young stellar objects, they tend to be quite saturated (hydrogen-rich) and terrestrial in nature. Based on both their spectra and chemistry, complex molecules are excellent probes of the physical conditions and history of the sources where they reside. Because they are detected in young stellar objects, complex molecules are expected to be common ingredients for new planetary systems. In this review, we discuss both the observation and chemistry of complex molecules in assorted interstellar regions in the Milky Way.