  It is now widely accepted that the cuprate superconductors are characterized
by the same long-range order as that present in the Bardeen-Cooper-Schrieffer
(BCS) theory: that associated with the condensation of Cooper pairs. We argue
that many physical properties of the cuprates require interplay with additional
order parameters associated with a proximate Mott insulator. We review a
classification of Mott insulators in two dimensions, and contend that the
experimental evidence so far shows that the class appropriate to the cuprates
has collinear spin correlations, bond order, and confinement of neutral, spin
S=1/2 excitations. Proximity to second-order quantum phase transitions
associated with these orders, and with the pairing order of BCS, has led to
systematic predictions for many physical properties. We use this context to
review the results of recent neutron scattering, fluxoid detection, nuclear
magnetic resonance, and scanning tunnelling microscopy experiments.
