The discovery of high prevalences of antibiotic resistance in some pathogens, in some parts of the world, has provoked fears of a widespread loss of drug efficacy. Here, we use a mathematical model to investigate the evolution of resistance to four major anti-tuberculosis drugs (isoniazid, rifampicin, ethambutol and streptomycin) in 47 sites around the world. The model provides a new method of estimating the relative risk of treatment failure for patients carrying drug–resistant strains and the proportion of patients who develop resistance after failing treatment. Using estimates of these two quantities together with other published data, we reconstructed the epidemic spread of isoniazid resistance over the past 50 years. The predicted median prevalence of resistance among new cases today was 7.0% (range 0.9–64.3%), close to the 6.3% (range 0–28.1%) observed. Predicted and observed prevalences of resistance to isoniazid plus rifampicin (multidrug–resistant or MDR–TB) after 30 years of combined drug use were also similar, 0.9% (0.1–5.9%) and 1.0% (range 0–14.1%), respectively.With current data, and under prevailing treatment practices, it appears that MDR–TB will remain a localized problem, rather than becoming a global obstacle to tuberculosis control. To substantiate this result, further measurements are needed of the relative fitness of drug–resistant strains.