Patients with cystic fibrosis (CF) are prone to developing life-threatening lung infections with a variety of pathogens that are difficult to eradicate, such as Burkholderia cepacia complex (Bcc), Hemophilus influenzae, Mycobacterium abscessus (Mab), Pseudomonas aeruginosa, and Staphylococcus aureus. These infections still remain an important issue, despite the therapy for CF having considerably improved in recent years. Moreover, prolonged exposure to antibiotics in combination favors the development and spread of multi-resistant bacteria; thus, the development of alternative strategies is crucial to counter antimicrobial resistance. In this context, phage therapy, i.e., the use of phages, viruses that specifically infect bacteria, has become a promising strategy. In this review, we aim to address the current status of phage therapy in the management of multidrug-resistant infections, from compassionate use cases to ongoing clinical trials, as well as the challenges this approach presents in the particular context of CF patients.