For tuberculosis to be eradicated, the transmission of Multi-Drug-Resistant and eXtensively Drug Resistant strains of Mycobacterium tuberculosis (MDR and XDR-TB) must be considerably reduced. Drug resistant strains were initially thought to have reduced fitness, and the majority of resistant strains may actually have compromised fitness because they are found in only one or a few patients. In contrast, some MDR/XDR-TB strains are highly transmitted and cause large outbreaks. Most antibiotics target essential bacterial functions and the mutations that confer resistance to anti-TB drugs can incur fitness costs manifested as slower growth and reduced viability. The fitness costs vary with different resistance mutations and the bacilli can also accumulate secondary mutations that compensate for the compromised functions and partially or fully restore lost fitness. The compensatory mutations (CM) are different for each antibiotic, as they mitigate the deleterious effects of the specific functions compromised by the resistance mutations. CM are generally more common in strains with resistance mutations incurring the greatest fitness costs, but for RIF resistance, CM are most frequent in strains with the mutation carrying the least fitness cost, Ser450Leu. Here, we review what is known about fitness costs, CM and mechanisms of resistance to the drugs that define a strain as MDR or XDR-TB. The relative fitness costs of the resistance mutations and the mitigating effects of CM largely explain why certain mutations are frequently found in highly transmitted clusters while others are less frequently, rarely or never found in clinical isolates. The CM illustrate how drug resistance affects bacteria and how bacteria evolve to overcome the effects of the antibiotics, and thus a paradigm for how mycobacteria can evolve in response to stress.