This paper extends conformal prediction to control the expectation of an arbitrary monotonic loss function. The algorithm generalizes split conformal prediction and its coverage guarantees. Similar to conformal prediction, the conformal risk control procedure is accurate up to $\mathcal{O}(1/n)$. In addition, we introduce distribution shift, quantile risk control, multi- and adversarial risk control, and an extension of the idea of the expectation of the U-statistic. We demonstrate the use of the algorithm to limit the false negative rate, graph distance, and token-level F1 score with real-world examples from computer vision and natural language processing.