Although early aggressive and prolonged treatment with specific antibiotics can extend survival in patients with cystic fibrosis (CF) colonized by opportunistic Pseudomonas aeruginosa (PA), antibiotics fail to eradicate the infecting multidrug-resistant (MDR) PA strains in CF. Century-long research has suggested treating patients with bacteriophages (phages, prokaryotic viruses) naturally hosted by bacteria. Although the only phage types used in therapy, lytic phages, lyse PA aggregated in biofilm matrix by depolymerase degrading enzymes, how they can effectively, safely, and persistently do so in patients with CF is unclear. Even though advanced techniques for formulating phage cocktails, training phages and collecting phage libraries have improved efficacy in vitro, whether personalized or ready-to-use therapeutic approaches or phages and antibiotics combined are effective and safe in vivo, and can reduce PA biofilms, remains debatable. Hence, to advance clinical research on phage therapy in clinical trials, also involving mucoid and non-mucoid multidrug-resistant PA in CF, and overcome problems in Western international regulations, we need reliable and repeatable information from experiments in vitro and in vivo on phage characterization, cocktail selection, personalized approaches, and phages combined with antibiotics. These findings, challenges, and promises prompted us to undertake this argumentative review to seek up-to-date information from papers describing lytic phage activity tested in vitro on PA laboratory strains, and PA strains from chronic infections including CF. We also reviewed in vivo studies on phage activity on pulmonary and non-pulmonary animal host models infected by laboratory or CF PA strains. Our argumentative review provides essential information showing that future phage clinical research in CF should use well-characterized and selected phages isolated against CF PA, tested in vitro under dynamic conditions in cocktails or combined with antibiotics, and in vivo on non-pulmonary and pulmonary host models infected with mucoid and non-mucoid CF MDR PA. Our findings should encourage pharmaceutical industries to conduct clinical trials in vitro and in vivo testing patented genomic engineered phages from phage libraries combined with antibiotics to treat or even prevent multidrug-resistant PA in CF, thus helping international regulatory agencies to plan future clinical research on phage therapy in CF.