Quasar outflows, in the form of broad-absorption line winds and radio jets, are likely to have left an indelible cosmological imprint. As energetic material from the densest objects in the centers of galaxies made its way into the intergalactic medium (IGM), it impacted structures on many scales, much as supernovae impact structures on many scales within the interstellar medium. Using simple analytical models, I will outline several observational features that are likely to have been caused by these interactions. As large regions of the IGM are shocked heated above a critical entropy of 100 keV cm^2, cooling becomes impossible within them, regardless of further changes in density. On quasar scales, this has the effect of inhibiting formation, resulting in the observed fall-off in their number densities below z = 2. On galaxy scales, quasar feedback fixes the turn-over scale in the galaxy luminosity function (L_*) as the nonlinear scale at the redshift of strong feedback. The galaxy luminosity function then remains largely fixed after this epoch, consistent with recent observations and in contrast to the strong evolution predicted in more standard galaxy-formation models. Finally, strong quasar feedback explains why the intracluster medium is observed to have been pre-heated to entropy levels just above the minimum excess that would not have been erased by cooling.