A major factor complicating efforts to control the tuberculosis epidemic is the long duration of treatment required to successfully clear the infection. One reason that long courses of treatment are required may be the fact that mycobacterial cells arise during the course of infection that are less susceptible to antibiotics. Here we describe the paradigms of phenotypic drug tolerance and resistance as they apply to mycobacteria. We then discuss the mechanisms by which phenotypically drug-tolerant and -resistant cells arise both at a population level and in specialized subpopulations of cells that may be especially important in allowing the bacterium to survive in the face of treatment. These include general mechanisms that have been shown to alter the susceptibility of mycobacteria to antibiotics including growth arrest, efflux pump induction, and biofilm formation. In addition, we discuss emerging data from single-cell studies of mycobacteria that have identified unique ways in which specialized subpopulations of cells arise that vary in their frequency, in their susceptibility to drug, and in their stability over time.