ABSTRACT. In this review we discuss the problems encountered in the design, implementation, and analysis of modern surveys aimed at discovering quasars. These fall into two broad categories: (1) the practical difficulties arising from the limited signal-to-noise ratio of the source material and the finite amount of telescope time available for follow-up observations, and (2) the challenges presented by the large ranges in the intrinsic properties of quasars, notably the spread in redshift, luminosity and spectral energy distributions. Three types of surveys are described, in order of increasing difficulty of implementation, the most challenging of which would both find quasars consistently and provide a prediction of those objects that would not be found. To achieve the scientific goals underlying such a survey, an accurate assessment of P (M, z, SED), the probability of detection of a quasar as a function of its absolute magnitude, redshift, and spectral energy distribution, must be made. We argue that the analyses of surveys at X-ray and radio wavelengths, as well as those based upon zero proper motion and photometric variability, should also contain such a calculation. If P (M, z, SED) is known, and is non-zero over a substantial range of one or more of the independent variables, then improved constraints on the form of the luminosity function can be obtained compared to those from many surveys which are ``complete'' in the traditional sense of the term. We highlight the need for accurate, broad-baseline measurements of quasar spectral energy distributions, which are necessary for a quantitative improvement in our knowledge of the evolution of the luminosity function.
Table of Contents