Entanglement in quantum field theory is in general very complicated. However, in large-N gauge theories dual to quantum gravity, it simplifies dramatically, and encodes detailed information about the spacetime geometry of the holographic dual. At low energy density, fluctuations of entanglement obey thermodynamic laws which can be recast as the Einstein equations in one extra dimension. At high energy density, entanglement encodes black hole geometries. I will give an overview of recent developments and discuss in some detail the structure of entanglement in two-dimensional conformal field theories.