  I discuss the impact of gauge-gravity duality on our understanding of two
classes of systems: conformal quantum matter and compressible quantum matter.
  The first conformal class includes systems, such as the boson Hubbard model
in two spatial dimensions, which display quantum critical points described by
conformal field theories. Questions associated with non-zero temperature
dynamics and transport are difficult to answer using conventional field
theoretic methods. I argue that many of these can be addressed systematically
using gauge-gravity duality, and discuss the prospects for reliable computation
of low frequency correlations.
  Compressible quantum matter is characterized by the smooth dependence of the
charge density, associated with a global U(1) symmetry, upon a chemical
potential. Familiar examples are solids, superfluids, and Fermi liquids, but
there are more exotic possibilities involving deconfined phases of gauge fields
in the presence of Fermi surfaces. I survey the compressible systems studied
using gauge-gravity duality, and discuss their relationship to the condensed
matter classification of such states. The gravity methods offer hope of a
deeper understanding of exotic and strongly-coupled compressible quantum
states.
