[For zoom link please contact s.nagyATqmul.ac.uk. There will be a pre-seminar for students at 13:30] The energy-energy correlation (EEC) measures the angular distribution of the energy that flows through two calorimeters separated by some relative angle in the final state created by a source. We present a new approach to computing this observable that exploits the relation between the energy correlations and four-point correlation functions of conserved currents. In the limit of small and large angles, when EEC describes the correlation between particles belonging, respectively, to the same jet and to two almost back-to-back jets, we obtain a concise representation of the EEC in terms of the conformal data of twist-two operators and verify it by comparing with the results of explicit calculation at next-to-next-to-leading order in maximally supersymmetric Yang-Mills theory. As a byproduct of our analysis, we predict the maximal weight part of the analogous QCD expression.