We present a new approach to computing energy-energy correlations (EEC) in gauge theories that exploits their relation to correlation functions and bypasses the use of scattering amplitudes. These infrared finite observables are familiar from collider physics studies and describe 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 illustrate the power of this approach by calculating energy-energy correlations in the maximally supersymmetric Yang-Mills theory (N=4 SYM) in the limit of small and large angles when it describes the correlation between particles belonging, respectively, to the same jet and to two almost back-to-back jets. In both cases, 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 calculations. As a byproduct of our analysis, we predict the maximal weight part of the analogous QCD expression in the back-to-back limit.