Some of the aspects of submillimeter-wave astronomy which are relevant to the field of heterodyne spectroscopy are reviewed. Most of the discussion concerns the dense interstellar medium where stars are forming, with some work presented on nearby galaxies. Extremely sensitive receivers, large accurate telescopes, and high-mountain, airborne, or space platforms are gradually being developed, so that information is steadily improving in quality and scope. Examples are given of line surveys of heavy molecule spectra, extending from millimeter wavelengths well into the submillimeter, of light molecule spectroscopy, and of atomic fine-structure spectroscopy. The importance of the spatial information on atomic and ionized carbon is discussed. The gas cooling process which allows clouds to collapse to form stars by means of the submillimeter line emission is discussed. Also covered are regions suffering shocks, photodissociation regions, and stellar outflow regions. Work on the submillimeter spectrum of nearby galaxies is briefly described. >