Predicting the functional sites of a protein from its structure, such as the binding sites of small molecules, other proteins or antibodies, sheds light on its function in vivo. Currently, two classes of methods prevail: machine learning models built on top of handcrafted features and comparative modeling. They are, respectively, limited by the expressivity of the handcrafted features and the availability of similar proteins. Here, we introduce ScanNet, an end-to-end, interpretable geometric deep learning model that learns features directly from 3D structures. ScanNet builds representations of atoms and amino acids based on the spatio-chemical arrangement of their neighbors. We train ScanNet for detecting protein–protein and protein–antibody binding sites, demonstrate its accuracy—including for unseen protein folds—and interpret the filters learned. Finally, we predict epitopes of the SARS-CoV-2 spike protein, validating known antigenic regions and predicting previously uncharacterized ones. Overall, ScanNet is a versatile, powerful and interpretable model suitable for functional site prediction tasks. A webserver for ScanNet is available from http://bioinfo3d.cs.tau.ac.il/ScanNet/.