  This article surveys the physics of systems proximate to Mott insulators, and
presents a classification using conventional and topological order parameters.
This classification offers a valuable perspective on a variety of conducting
correlated electron systems, from the cuprate superconductors to the heavy
fermion compounds. Connections are drawn, and distinctions made, between
collinear/non-collinear magnetic order, bond order, neutral spin 1/2
excitations in insulators, electron Fermi surfaces which violate Luttinger's
theorem, fractionalization of the electron, and the fractionalization of
bosonic collective modes. Two distinct categories of Z_2 gauge theories are
used to describe the interplay of these orders. Experimental implications for
the cuprates are briefly noted, but these appear in more detail in a companion
review article (S. Sachdev, cond-mat/0211005).
