Hydride complexes of copper, silver, and gold encompass a broad array of structures, and their distinctive reactivity has enabled dramatic recent advances in synthesis and catalysis. This Review summarizes the synthesis, characterization, and key stoichiometric reactions of isolable or observable coinage metal hydrides. It discusses catalytic processes in which coinage metal hydrides are known or probable intermediates, and presents mechanistic studies of selected catalytic reactions. The purpose of this Review is to convey how developments in coinage metal hydride chemistry have led to new organic transformations, and how developments in catalysis have in turn inspired the synthesis of reactive new complexes.