Antimicrobial resistance (AMR) is a global public-health emergency, which threatens the advances made by modern medical care over the past century. The World Health Organization has recently published a global priority list of antibiotic-resistant bacteria, which includes extended-spectrum β-lactamase-producing Enterobacteriaceae and carbapenemase-producing Enterobacteriaceae. In this review, we highlight the mechanisms of resistance and the genomic epidemiology of these organisms, and the impact of AMR.