Rabies virus causes nearly 60,000 human deaths annually. Antibodies that target the rabies glycoprotein (G) are being developed as post-exposure prophylactics, but mutations in G can render such antibodies ineffective. Here, we use pseudovirus deep mutational scanning to measure how all single-amino-acid mutations to G affect cell entry and neutralization by a panel of antibodies. These measurements identify sites critical for G function and define constrained regions that are attractive epitopes for clinical antibodies, including at the apex and base of the protein. We provide complete maps of escape mutations for eight monoclonal antibodies, including some in clinical use or development. Escape mutations for most antibodies are present in some natural rabies strains. Overall, this work provides comprehensive information on the functional and antigenic effects of G mutations that can inform development of stabilized vaccine antigens and antibodies that are resilient to rabies genetic variation.