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The problem presented by polyatomic molecules in interstellar space were first suggested by the detection of CN, CH, and CH+ just before 1940; but it was not until the discovery of radio emission from NH3 in 1968 that radio observatories began to devote considerable time to searches for such molecules. The quest has been an extremely successful one, with well over thirty molecules listed to date and more being added to the collection every month. (The list in the appendix gives some idea of the discoveries, but makes no boast as to its completeness.)