The common theme of these DFTs is the reduction of the inherent complexity of the direct description of a many-body system to the comparative simplicity of functionals of the density -either explicitly, or implicitly in terms of auxiliary functions such as orbitals. The strategy, in the time-independent case at least, is to obtain the relevant physics (hence also chemistry) by an appropriate minimization procedure on a functional of the density itself (whether it be pure-state or ensemble).