Recent reports of extensively drug-resistant TB in South Africa have renewed concerns that antibiotic resistance may undermine progress in TB control. We review three major questions for which mathematical models elucidate the epidemiology and control of drug-resistant TB. How is multiple drug-resistant Mycobacterium tuberculosis selected for in individuals exposed to combination chemotherapy? What factors determine the prevalence of drug-resistant TB? Which interventions to prevent the spread of drug-resistant TB are effective and feasible? Models offer insight into the acquisition and amplification of drug resistance, reveal the importance of distinguishing the intrinsic and extrinsic determinants of the reproductive capacity of drug-resistant M. tuberculosis, and demonstrate the cost effectiveness of interventions for drug-resistant TB. These models also highlight knowledge gaps for which new research will improve our ability to project trends of drug resistance and develop more effective policies for its control.