At present, the successful transmission of drug‐resistant Mycobacterium tuberculosis, including multidrug‐resistant (MDR) and extensively drug‐resistant (XDR) strains, in human populations, threatens tuberculosis control worldwide. Differently from many other bacteria, M. tuberculosis drug resistance is acquired mainly through mutations in specific drug resistance‐associated genes. The panel of mutations is highly diverse, but depends on the affected gene and M. tuberculosis genetic background. The variety of genetic profiles observed in drug‐resistant clinical isolates underlines different evolutionary trajectories towards multiple drug resistance, although some mutation patterns are prominent. This review discusses the intrinsic processes that may influence drug resistance evolution in M. tuberculosis, such as mutation rate, drug resistance‐associated mutations, fitness cost, compensatory mutations and epistasis. This knowledge should help to better predict the risk of emergence of highly resistant M. tuberculosis strains and to develop new tools and strategies to limit the development and spread of MDR and XDR strains.