Although astronomical molecules can be obtained from samples of matter from comets and asteroids, the means by which the overwhelming numbers of discoveries are made is through spectroscopy. Very many of these discoveries are made using rotational spectra of molecules with transitions at millimetre wavelengths. Some species are detected in the infrared through vibrational transitions, while a very small number of species are detected via electronic transitions lying in the optical and ultraviolet regions. We revise briefly how these spectra arise. At first, it seems that an enormous number of transitions are available for observation; however, a discussion of the so-called critical number density shows that in practice the number of appropriate transitions for particular physical conditions is greatly reduced. The chapter ends with a concise discussion of radiative transfer.