deconfined phases, signaled by a change in the value of the Wilson loop of the gauge field from area law to perimeter law. Wegner also argued that confinement transition of this theory had no local order parameter, but was instead described by a dual Ising model in 3 dimensions. This conclusion turns out to need a crucial extension. One of the implications of Sachdev's work on emergent gauge fields in two-dimensional antiferromagnets was that the deconfined phase of the 2+1 dimensional Ising gauge theory had Z2 topological order. The presence of topological order in one of the phases implies that this is an Ising* transition, in which we only select states and operators which are invariant under global Ising inversion; see a recent numerical study for observable consequences of this restriction. The Ising field represents a fractionalized excitation of the deconfined phase, the "vison" (or the m particle) carrying a quantum of Z2 gauge flux, and visons can only be created in pairs. The confinement transition is driven by the condensation of deconfined visons, and so this is an example of a deconfined quantum critical point, although there is no gapless gauge field. Odd Ising gauge theories: The notion of deconfined criticality becomes more crucial in studying the confinement transitions of RVB states. These are described by deconfined phases of "odd" Ising gauge theories with Z2 topological order. (Wegner's Z2 gauge theory, which is "even", is not a satisfactory theory of the RVB state.) Now the critical theory has fractionalized excitations and a gapless gauge field. In the context of two-dimensional antiferromagnets with half-integer spin per unit cell, the effective description in terms of Ising gauge theories requires a background static electric charge on each site: this is the odd Ising gauge theory. We can write the Ising gauge theory as the strong coupling limit of a compact U(1) gauge theory in the presence of a charge 2 Higgs field. The presence of the background electric charges implies that the monopoles of the U(1) field carry Berry phases, and transform non-trivially under the space group of the lattice. As the monopoles condense in the confining phase, an immediate consequence is that the confining phase must break the space group by the development of valence bond solid (VBS) order. Furthermore, the Berry phases lead to suppression of monopoles at the critical point, so that, on the square lattice, the critical theory