Klebsiella spp. are commensals of the human microbiota, and a leading cause of opportunistic nosocomial infections. The incidence of multidrug resistant (MDR) strains of Klebsiella pneumoniae causing serious infections is increasing, and Klebsiella oxytoca is an emerging pathogen. Alternative strategies to tackle infections caused by these bacteria are required as strains become resistant to last-resort antibiotics such as colistin. Bacteriophages (phages) are viruses that can infect and kill bacteria. They and their gene products are now being considered as alternatives or adjuncts to antimicrobial therapies. Several in vitro and in vivo studies have shown the potential for lytic phages to combat MDR K. pneumoniae infections. Ready access to cheap sequencing technologies has led to a large increase in the number of genomes available for Klebsiella -infecting phages, with these phages being heterogeneous at the whole-genome level. This review summarizes our current knowledge on phages of Klebsiella spp. and highlights technological and biological issues relevant to the development of phage-based therapies targeting these bacteria.