The rise in gonococcal antibiotic resistance and the threat of untreatable infection are focusing attention on strategies to limit the spread of drug-resistant gonorrhea. Mathematical models provide a framework to link the natural history of infection and patient behavior to epidemiological outcomes and can be used to guide research and enhance the public health impact of interventions. While limited knowledge of key disease parameters and networks of spread has impeded development of operational models of gonococcal transmission, new tools in gonococcal surveillance may provide useful data to aid tracking and modeling. Here, we highlight critical questions in the management of gonorrhea that can be addressed by mathematical models and identify key data needs. Our overarching aim is to articulate a shared agenda across gonococcus-related fields from microbiology to epidemiology that will catalyze a comprehensive evidence-based clinical and public health strategy for management of gonococcal infections and antimicrobial resistance.