The continued rise in antimicrobial resistance poses a serious threat to public health worldwide. The use of phages that can have bactericidal activity without disrupting the normal flora represents a promising alternative treatment method. This practice has been successfully applied for decades, mainly in Eastern Europe, and has recently been used as an emergency therapy for compassionate care in the United States. Here, we provide a comprehensive review of the pre-clinical and clinical applications of phage therapy concerning three major Gram-negative pathogens: Klebsiella pneumoniae, Pseudomonas aeruginosa, and Acinetobacter baumannii. The advantages and the challenges of expanding the usage of phages as an alternative or adjunctive treatment for antimicrobial-resistant bacterial infections are discussed. We emphasize the virologic complexities of using the highly adaptable phage populations as molecular tools, along with antibiotic chemical compounds, to effectively combat rapidly coevolving pathogenic bacteria in the host microenvironment. Pre-clinical studies, isolated clinical reports and a few randomized clinical trials have shown that bacteriophages can be effective in treating multidrug-resistant bacterial infections. The ability of some phages to revert the resistance against antibiotics, and possibly also against the human complement and other phages, appears to be a great advantage of phage therapy despite the inevitable emergence of phage-resistant strains. Bacteriophages (or specific phage-derived products) can enhance antimicrobial efficacy by reducing bacterial virulence via the alteration of basic bacterial structures, primarily of the cellular wall and membrane. Although several issues remain open regarding their effective clinical application, it appears that phage-based therapeutics in combination with antibiotics can provide an effective solution to the spread of antimicrobial resistance.