  The last few years have seen significant experimental progress in
characterizing the copper-based hole-doped high temperature superconductors in
the regime of low hole density, p. Quantum oscillations, NMR, X-ray, and STM
experiments have shed much light on the nature of the ordering at low
temperatures. We review evidence that the order parameter in the
non-Lanthanum-based cuprates is a d-form factor density-wave. This novel order
acts as an unexpected window into the electronic structure of the pseudogap
phase at higher temperatures in zero field: we argue in favor of a
`fractionalized Fermi liquid' (FL*) with 4 pockets of spin S=1/2, charge +e
fermions enclosing an area specified by p.
