Negative energy density can arise naturally in Quantum Field Theory, the theoretical framework with which we describe fundamental particle physics and the matter which makes up our universe. However too much negative energy density can lead to pathologies when considering the dynamics of spacetime in which this matter resides. This dynamics is governed by Einstein’s equations which relates such energy densities to the curvature of spacetime. In this talk I will discuss conjectured bounds on negative energy density and sketch very recent general proofs of these bounds. The methods we use combine causality considerations with concepts taken from the study of quantum information.