Abstract
This review discusses the H3+ molecular ion and its deuterated isotopomers. The ion is important because of its fundamental nature, astrophysical significance and dynamical richness. The following topics are discussed: the discovery of H3+, its unusual bonding and the important role played by ab initio electronic-structure calculations; the formation of H3+ and its importance in models of the interstellar medium; the unusual spectroscopy of H3+ and the accurate quantum calculations which led to laboratory observations; the failure to detect H3+ in the interstellar medium and its accidental observation in Jupiter; work on H3+ in the giant planets and other astronomical emission spectra; the very unusual infrared photodissociation spectrum of H3+; and the classical and quantal behaviour of the molecule at its dissociation limit.