Pseudomonas aeruginosa is a frequent participant in wound infections. Emergence of multiple antibiotic resistant strains has created significant problems in the treatment of infected wounds. Phage therapy (PT) has been proposed as a possible alternative approach. Infected wounds are the perfect place for PT applications, since the basic condition for PT is ensured; namely, the direct contact of bacteria and their viruses. Plenty of virulent (“lytic”) and temperate (“lysogenic”) bacteriophages are known in P. aeruginosa. However, the number of virulent phage species acceptable for PT and their mutability are limited. Besides, there are different deviations in the behavior of virulent (and temperate) phages from their expected canonical models of development. We consider some examples of non-canonical phage-bacterium interactions and the possibility of their use in PT. In addition, some optimal approaches to the development of phage therapy will be discussed from the point of view of a biologist, considering the danger of phage-assisted horizontal gene transfer (HGT), and from the point of view of a surgeon who has accepted the Hippocrates Oath to cure patients by all possible means. It is also time now to discuss the possible approaches in international cooperation for the development of PT. We think it would be advantageous to make phage therapy a kind of personalized medicine.