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Biophysical interactions between proteins and peptides are key determinants of molecular recognition specificity landscapes. However, an understanding of how molecular structure and residue-level energetics at protein−peptide interfaces shape these landscapes remains elusive. We combine information from yeast-based library screening, next-generation sequencing, and structure-based modeling in a supervised machine learning approach to report the comprehensive sequence−energetics−function mapping of the specificity landscape of the hepatitis C virus (HCV) NS3/4A protease, whose function—site-specific cleavages of the viral polyprotein—is a key determinant of viral fitness. We screened a library of substrates in which five residue positions were randomized and measured cleavability of ∼30,000 substrates (∼1% of the library) using yeast display and fluorescence-activated cell sorting followed by deep sequencing. Structure-based models of a subset of experimentally derived sequences were used in a supervised learning procedure to train a support vector machine to predict the cleavability of 3.2 million substrate variants by the HCV protease. The resulting landscape allows identification of previously unidentified HCV protease substrates, and graph-theoretic analyses reveal extensive clustering of cleavable and uncleavable motifs in sequence space. Specificity landscapes of known drug-resistant variants are similarly clustered. The described approach should enable the elucidation and redesign of specificity landscapes of a wide variety of proteases, including human-origin enzymes. Our results also suggest a possible role for residue-level energetics in shaping plateau-like functional landscapes predicted from viral quasispecies theory.