The SARS-CoV-2 main protease (Mpro) is essential to viral replication and cleaves highly specific substrate sequences, making it an obvious target for inhibitor design. However, as for any virus, SARS-CoV-2 is subject to constant neutral drift and selection pressure, with new Mpro mutations arising over time. Identification and structural characterization of Mpro variants is thus critical for robust inhibitor design. Here we report sequence analysis, structure predictions, and molecular modeling for seventy-nine Mpro variants, constituting all clinically observed mutations in this protein as of April 29, 2020. Residue substitution is widely distributed, with some tendency toward larger and more hydrophobic residues. Modeling and protein structure network analysis suggest differences in cohesion and active site flexibility, revealing patterns in viral evolution that have relevance for drug discovery.