Antibiotic treatment failure is of growing concern. Genetically encoded resistance is key in driving this process. However, there is increasing evidence that bacterial antibiotic persistence, a non-genetically encoded and reversible loss of antibiotic susceptibility, contributes to treatment failure and emergence of resistant strains as well. In this Review, we discuss the evolutionary forces that may drive the selection for antibiotic persistence. We review how some aspects of antibiotic persistence have been directly selected for whereas others result from indirect selection in disparate ecological contexts. We then discuss the consequences of antibiotic persistence on pathogen evolution. Persisters can facilitate the evolution of antibiotic resistance and virulence. Finally, we propose practical means to prevent persister formation and how this may help to slow down the evolution of virulence and resistance in pathogens.