Pseudomonas aeruginosa is a leading cause of persistent and severe lung infections, especially in individuals with weakened immune systems and those suffering from conditions like cystic fibrosis or bronchiectasis. The pathogen’s resistance to antibiotics, driven by its ability to form biofilms, activate efflux pumps, and produce enzymes that break down drugs, has significantly limited the effectiveness of standard antimicrobial therapies. This review explores the increasing promise of bacteriophage therapy as both an alternative and a complementary approach for addressing multidrug-resistant (MDR) P. aeruginosa infections in the lungs. Phages, viruses that specifically target bacteria, offer strain-specific bactericidal activity, often bypassing mechanisms of antibiotic resistance. Recent studies demonstrate that phage monotherapy and phage-antibiotic combinations can effectively disrupt biofilms and enhance bacterial clearance, particularly when phage cocktails or targeted delivery systems are employed. Additionally, the review explores delivery routes for pulmonary infections and the formulation challenges that affect phage stability and bioavailability. Clinical cases and ongoing trials further underscore the feasibility and safety of phage therapy in real-world applications. However, hurdles such as phage immunogenicity, rapid clearance, and regulatory limitations must be addressed before widespread clinical implementation. Overall, phage therapy holds significant promise in overcoming the therapeutic stagnation posed by MDR P. aeruginosa, especially in chronic and nosocomial lung infections, and warrants continued research and clinical validation.