Antimicrobial-resistant Klebsiella pneumoniae (Kp) has emerged as a major global public health problem. While resistance can occur across a broad range of Kp clones, a small number have become globally distributed and commonly cause outbreaks in hospital settings. Here we describe recent comparative genomics investigations that have shed light on Kp population structure and the evolution of antimicrobial-resistant clones. These studies provide the basic framework within which genomic epidemiology and evolution can be understood, but have merely scratched the surface of what can and should be explored. We assert that further large-scale comparative and functional genomics studies are urgently needed to better understand the biology of this clinically important bacterium.