The chemical composition and structure of envelopes surrounding cool evolved stars, as determined from microwave spectroscopic observations, is reviewed. Emphasis is placed on recent observations with the new large mm-wavelength telescopes and interferometer arrays, and on new theoretical work, especially concerning ion-molecule chemistry in these envelopes. Thermal (as opposed to maser) emission lines are discussed. Much progress has been made in the past few years in the theoretical understanding of these objects. It is already clear, however, that observations with the new generation of mm-telescopes will require substantial improvements in the theoretical models to achieve a thorough understanding of the data now becoming available.