Staphylococcus aureus (S. aureus) is a common and virulent human pathogen causing several serious illnesses including skin abscesses, wound infections, endocarditis, osteomyelitis, pneumonia, and toxic shock syndrome. Antibiotics were first introduced in the 1940s, leading to the belief that bacterial illnesses would be eradicated. However, microorganisms, including S. aureus, began to develop antibiotic resistance from the increased use and abuse of antibiotics. Antibiotic resistance is now one of the most serious threats to global public health. Bacteria like methicillin-resistant Staphylococcus aureus (MRSA) remain a major problem despite several efforts to find new antibiotics. New treatment approaches are required, with bacteriophage treatment, a non-antibiotic strategy to treat bacterial infections, showing particular promise. The ability of S. aureus to resist a wide range of antibiotics makes it an ideal candidate for phage therapy studies. Bacteriophages have a relatively restricted range of action, enabling them to target pathogenic bacteria. Their usage, usually in the form of a cocktail of bacteriophages, allows for more focused treatment while also overcoming the emergence of resistance. However, many obstacles remain, particularly in terms of their effects in vivo, necessitating the development of animal models to assess the bacteriophage efficiency. Here, we provide a review of the animal models, the various clinical case treatments, and clinical trials for S. aureus phage therapy.