  We present a review of theories of states of quantum matter without
quasiparticle excitations. Solvable examples of such states are provided
through a holographic duality with gravitational theories in an emergent
spatial dimension. We review the duality between gravitational backgrounds and
the various states of quantum matter which live on the boundary. We then
describe quantum matter at a fixed commensurate density (often described by
conformal field theories), and also compressible quantum matter with variable
density, providing an extensive discussion of transport in both cases. We
present a unified discussion of the holographic theory of transport with memory
matrix and hydrodynamic methods, allowing a direct connection to experimentally
realized quantum matter. We also explore other important challenges in
non-quasiparticle physics, including symmetry broken phases such as
superconductors and non-equilibrium dynamics.
