We review the role of self-consistency in density functional theory (DFT). We apply a recent analysis to both Kohn-Sham and orbital-free DFT, as well as to partition DFT, which generalizes all aspects of standard DFT. In each case, the analysis distinguishes between errors in approximate functionals versus errors in the self-consistent density. This yields insights into the origins of many errors in DFT calculations, especially those often attributed to self-interaction or delocalization error. In many classes of problems, errors can be substantially reduced by using better densities. We review the history of these approaches, discuss many of their applications, and give simple pedagogical examples.
Keywords: DC-DFT; binding curves; electron affinity; embedding; error analysis; fragmentation methods; partition DFT; potential energy surfaces.