The AdS/CFT duality between a (gravitational) string theory and a (non gravitational) quantum field theory has given rise to the profound idea that spacetime and gravity can emerge from the physics of quantum entanglement - a uniquely quantum mechanical correlation between distant physical systems. Evidence in favor of this paradigm for the emergence of gravity will be presented. Firstly, I will discuss how Einstein’s equations, describing amongst other things the propagation of gravity waves, can be re-written as a thermodynamical first law for entanglement entropy. Secondly, under the duality, I will relate the fact that entanglement in the quantum system cannot be used to communicate faster than the speed of light to the fact that exotic matter, allowing large amounts of negative energy density, should not exist. Such matter could be used to violate causality in the gravitational theory. We recently ruled out such exotic matter by proving a conjectured bound on the energy density of a general class of quantum field theories called the quantum null energy condition.