A useful instrument to quantify the activity statistics of AGN is their luminosity function (LF). Only five years ago, there was still confusion about the evolutionary pattern of the type-1 LF. While a strong increase of the activity out to z ~ 2 had been established a long time before, and a turnover must be trivially expected at higher redshift somewhere, the shape of the turnover and the redshift of any peak in activity was still unclear. Boyle, Shanks & Peterson (1988) described the LF at z = [0.3, 2.2] with a broken power-law, characterized by the parameters L*(z) and *(z). These allowed to distinguish between simple evolutionary models such as Pure Luminosity Evolution (PLE) and Pure Density Evolution (PDE), with PLE being the preferred description for the low-redshift (z < 2) evolution of QSOs. At high redshift z = [2.7, 4.7] Schmidt, Schneider & Gunn (1995) parametrized the LF with a single power-law that does not feature any break luminosity, because their small sample and narrow luminosity range did not constrain any more parameters. In their L-range they found a strong decrease in the activity when going towards higher redshift. Finally, Warren, Hewitt & Osmer (1994) bridged the gap and investigated the turnover within z = [2.0, 4.5]. Their model fit followed a complicated description of luminosity-dependent density evolution (LDDE) with a strong high-redshift cutoff at z > 3.3.
While the rise and fall of quasars between the Big Bang and today was established by these observations, there was still disagreement on the shape and redshift of the turnover. E.g., at z = [2.2, 3.6] the selection of QSOs from colours was difficult due to abundant stars having similar colours as the rare QSOs, and hence quantifying the selection function carefully was nearly impossible. Furthermore, each QSO sample at z > 2 contained only a few dozen objects across a narrow luminosity range, which left the shape of the LF unconstrained (for details see Osmer 2003 and references therein). Clearly, larger surveys mapping the luminosity-redshift plane as widely as possible were needed to advance the field of QSO evolution.