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One useful observable for studying QFT dynamics is the correlation between the total energy flux emitted in different directions from some local source. I will discuss the computation of these energy correlators in the specific case of conformal field theories, where they can be obtained as a sum over conformal blocks. After reviewing some general properties of energy correlators in CFTs, I will show how they can be used to derive novel bounds on OPE coefficients involving the stress-energy tensor.