  The critical theory of the onset of antiferromagnetism in metals, with
concomitant Fermi surface reconstruction, has recently been shown to be
strongly coupled in two spatial dimensions. The onset of unconventional
superconductivity near this critical point is reviewed: it involves a subtle
interplay between the breakdown of fermionic quasiparticle excitations on the
Fermi surface, and the strong pairing glue provided by the antiferromagnetic
fluctuations. The net result is a logarithm-squared enhancement of the pairing
vertex for generic Fermi surfaces, with a universal dimensionless co-efficient
independent of the strength of interactions, which is expected to lead to
superconductivity at the scale of the Fermi energy. We also discuss the
possibility that the antiferromagnetic critical point can be replaced by an
intermediate `fractionalized Fermi liquid' phase, in which there is Fermi
surface reconstruction but no long-range antiferromagnetic order. We discuss
the relevance of this phase to the underdoped cuprates and the heavy-fermion
materials.
