Spectral factorization is a crucial step in the solution of linear quadratic estimation and control problems. It is no wonder that a variety of methods has been developed over the years for the computation of canonical spectral factors. This paper provides a survey of several of these methods with special emphasis on clarifying the connections that exist among them. While the discussion focuses primarily on scalar-valued rational spectra, extensions to non-rational and vector-valued spectra are briefly noted. Copyright © 2001 John Wiley & Sons, Ltd.