Although base editors are widely used to install targeted point mutations, the factors that determine base editing outcomes are not well understood. We characterized sequence-activity relationships of 11 cytosine and adenine base editors (CBEs and ABEs) on 38,538 genomically integrated targets in mammalian cells and used the resulting outcomes to train BE-Hive, a machine learning model that accurately predicts base editing genotypic outcomes (R ≈ 0.9) and efficiency (R ≈ 0.7). We corrected 3,388 disease-associated SNVs with ≥90% precision, including 675 alleles with bystander nucleotides that BE-Hive correctly predicted would not be edited. We discovered determinants of previously unpredictable C-to-G, or C-to-A editing and used these discoveries to correct coding sequences of 174 pathogenic transversion SNVs with ≥90% precision. Finally, we used insights from BE-Hive to engineer novel CBE variants that modulate editing outcomes. These discoveries illuminate base editing, enable editing at previously intractable targets, and provide new base editors with improved editing capabilities. Display omitted •Base editing outcome precision and efficiency are frequently unintuitive•Machine learning model (BE-Hive) accurately predicts base editing efficiency and editing patterns•Base editor engineering can increase and reduce aberrant transversion editing•We precisely correct 3,388 pathogenic SNVs, many previously considered intractable A comprehensive look at CRISPR base editing efficiencies and outcomes across target sequences, cell lines, and base editing effectors yields machine learning models and a web-based tool for users to predict the editing efficiency, bystander edits, and the best base editor to use for a sequence of interest.