Predicting interactions between proteins and other biomolecules purely based on structure is an unsolved problem in biology. A high-level description of protein structure, the molecular surface, displays patterns of chemical and geometric features that may reveal a protein’s modes of interactions with other biomolecules. We hypothesize that these patterns engrave proteins with interaction fingerprints, such that proteins performing similar interactions share common fingerprints, independent of their amino acid sequence. Fingerprints may be difficult grasp by visual analysis but could be learned from large-scale datasets. We present a conceptual framework based on a new geometric deep learning method to capture fingerprints that are important for specific interactions. We showcase our method with tests on three fundamental aspects in biomolecular interactions: protein pocket-ligand prediction, protein-protein interaction site prediction, and ultrafast scanning of protein surfaces for prediction of protein-protein complexes. We anticipate that our conceptual framework will lead to improvements in our understanding of protein function and design.