Many modern materials, including the high temperature superconductors, display quantum critical points where the electron wavefunction is “entangled”, so that the low energy excitations cannot be described in a quasiparticle basis. I will describe recent progress in understanding the physics of such critical points, using quantum field theory, string theory, and quantum Monte Carlo simulations. I argue that these advances shed light on many of the puzzling features of the phase diagrams of the high temperature superconductors.