Many classical field theories satisfy various positive conditions for the stress-energy tensor. These conditions are crucial for example in singularity theorems of Penrose and Hawking. On the contrary, quantum stress energy tensors necessarily violate all such positivity conditions and admit negative expectation values. Surprisingly, there is still some reminiscence of the nice classical behavior: negative energy cannot last very long. This phenomenon is described by so-called averaged energy inequalities. I will talk about the work of Christopher Fewster on this subject.