Ever since the spectrum of a supernova was first observed in 1885, astronomers have known that a correct reading of the spectrum would reveal otherwise unattainable information about the physical conditions and composition of the radiation source. But the spectra of supernovae resisted interpretation for a very long time. The outstanding obstacle was the great characteristic width of the spectral features-150-300 A-corresponding to Doppler broadening velocities of 5000-10,000 km S-l. Because only a dozen or so overlapping spectral features occupy the whole optical spectrum at anyone time, line identifications proved to be so difficult that very little was known about Type II spectra, and even less about Type I, until around 1970. In the hope that a brief history of the subject will be interesting (if not of great utility), I attempt in Section 2.2 to outline the development of supernova spectrum interpretations, and to cite in one place most of the significant papers. Section 2.3 then presents a list of classifications of all supernovae whose spectra I have seen, and a (nearly) complete spectrum bibliography.We now know that during the first months after an explosion the ejected matter remains optically thick; "P Cygni" profiles of spectral lines formed in the outer layers are superimposed on a thermal continuum emitted from a photosphere, and spectrum formation is analagous to that which occurs in an expanding stellar atmosphere. As the ejected matter becomes optically thin to continuum photons via expansion and cooling, the supernova gradually becomes a self-excited nebula, with emission lines dominating the spectrum. In Section 2.4, the basic theory of spectrum formation during the photospheric and nebular phases, and methods for calculating synthetic spectra that were developed before the time ofSN 1987A, are reviewed in qualitative terms. As summarized in Section 2.5, it was only during the early 1980s that the classical mysteries of supernova spectra were fully resolved-definite line identifications were established and a good semiquantitative picture of spectrum formation was achieved. Now the spectra of supernova 1987 A are stimulating the development of more detailed, quantitative analyses. The techniques now being tested on SN 1987 A are likely to lead in a few years to reliable information on the composition of the matter ejected by supernovae of all types-information which will have a strong impact on attempts to relate the various kinds of supernovae to their stellar progenitors and explosion mechanisms. The first applications of the new quantitative spectroscopy, and the prospects for further work, are discussed briefly in Section 2.6.A. G. Petschek (ed.), Supernovae