Drug-insensitive tumor subpopulations remain a significant barrier to effective cancer treatment. Recent works suggest that within isogenic drug-sensitive cancer populations, subsets of cells can enter a 'persister' state allowing them to survive prolonged drug treatment. Such persisters are well-described in antibiotic-treated bacterial populations. In this review, we compare mechanisms of drug persistence in bacteria and cancer. Both bacterial and cancer persisters are associated with slow-growing phenotypes, are metabolically distinct from non-persisters, and depend on the activation of specific regulatory programs. Moreover, evidence suggests that bacterial and cancer persisters are an important reservoir for the emergence of drug-resistant mutants. The emerging parallels between persistence in bacteria and cancer can guide efforts to untangle mechanistic links between growth, metabolism, and cellular regulation, and reveal exploitable therapeutic vulnerabilities.