The paper describes some results and methods of work on the submillimeter spectrum and its application to atmospheric and astrophysical problems. The paper begins with descriptions of the spectroscopic techniques evolved and used, which provide spectral resolution more than half an order of magnitude finer than previously available, particularly at the lower frequency end of the range. Excellent signal-to-noise ratios and reproducibility have been obtained and applied to both atmospheric studies and astrophysical problems. The former are illustrated with aircraft-borne measurements of minor species, such as H2O, O3, HNO3, and other gases, the latter with a consideration of the cosmic background at submillimeter wavelengths. A common thread is provided by developments in observational and interpretational spectroscopic techniques needed to overcome problems peculiar to this region of the spectrum.