Effective control of an epidemic relies on the rapid discovery and isolation of infected individuals. Because many infectious diseases spread through interaction, contact tracing is widely used to facilitate case discovery and control. However, what determines the efficacy of contact tracing has not been fully understood. Here we reveal that, compared with ‘forward’ tracing (tracing to whom disease spreads), ‘backward’ tracing (tracing from whom disease spreads) is profoundly more effective. The effectiveness of backward tracing is due to simple but overlooked biases arising from the heterogeneity in contacts. We argue that, even if the directionality of infection is unknown, it is possible to perform backward-aiming contact tracing. Using simulations on both synthetic and high-resolution empirical contact datasets, we show that strategically executed contact tracing can prevent a substantial fraction of transmissions with a higher efficiency—in terms of prevented cases per isolation—than case isolation alone. Our results call for a revision of current contact-tracing strategies so that they leverage all forms of bias. It is particularly crucial that we incorporate backward and deep tracing in a digital context while adhering to the privacy-preserving requirements of these new platforms.