The current emergence of multi-, extensively-, extremely-, and total-drug resistant strains of Mycobacterium tuberculosis poses a major health, social, and economic threat, and stresses the need to develop new therapeutic strategies. The notion of phage therapy against bacteria has been around for more than a century and, although its implementation was abandoned after the introduction of drugs, it is now making a comeback and gaining renewed interest in Western medicine as an alternative to treat drug-resistant pathogens. Mycobacteriophages are genetically diverse viruses that specifically infect mycobacterial hosts, including members of the M. tuberculosis complex. This review describes general features of mycobacteriophages and their mechanisms of killing M. tuberculosis, as well as their advantages and limitations as therapeutic and prophylactic agents against drug-resistant M. tuberculosis strains. This review also discusses the role of human lung micro-environments in shaping the availability of mycobacteriophage receptors on the M. tuberculosis cell envelope surface, the risk of potential development of bacterial resistance to mycobacteriophages, and the interactions with the mammalian host immune system. Finally, it summarizes the knowledge gaps and defines key questions to be addressed regarding the clinical application of phage therapy for the treatment of drug-resistant tuberculosis.