The observed spectrum of a galaxy is the composite spectrum of its stellar population broadened by the stellar velocities. Our topic is the extraction of the broadening functions (i.e., line-of-sight velocity distributions) from spectra. In the past, observers tried to extract only mean velocities and dispersions. But recent work on deconvolution [Franx & Illingworth ApJL327, L55 (1989), Bender A&A229, 441 (1990), Rix & White MNRAS254, 389 (1992), van der Marel & Franx ApJ, to appear] shows that more information can be recovered. The general idea is to compare a galaxy spectrum with one or more stellar ‘template’ spectra; but various methods differ widely in the treatment of noise and the control of sources of systematic error.