  We discuss fluctuating order in a quantum disordered phase proximate to a
quantum critical point, with particular emphasis on fluctuating stripe order.
Optimal strategies for extracting information concerning such local order from
experiments are derived with emphasis on neutron scattering and scanning
tunneling microscopy. These ideas are tested by application to two model
systems - the exactly solvable one dimensional electron gas with an impurity,
and a weakly-interacting 2D electron gas. We extensively review experiments on
the cuprate high-temperature superconductors which can be analyzed using these
strategies. We adduce evidence that stripe correlations are widespread in the
cuprates. Finally, we compare and contrast the advantages of two limiting
perspectives on the high-temperature superconductor: weak coupling, in which
correlation effects are treated as a perturbation on an underlying metallic
(although renormalized) Fermi liquid state, and strong coupling, in which the
magnetism is associated with well defined localized spins, and stripes are
viewed as a form of micro-phase separation. We present quantitative indicators
that the latter view better accounts for the observed stripe phenomena in the
cuprates.
