Phage therapy, a promising alternative to antimicrobial treatment of bacterial diseases, is getting more and more popular, especially due to the rising awareness of antibiotic resistance and restrictions in antibiotics’ use. During recent years, we observed a growing trend of bacteriophages’ application in aquaculture, which in each year reports high losses due to bacterial diseases. This review provides an update of the status of bacteriophage therapy for the treatment and prevention of infections in the aquatic environment. As it is still mostly in the scientific stage, there are a few constraints that may prevent effective therapy. Therefore, specific characteristics of bacteriophages, that can act in favor or against their successful use in treatment, were described. We underlined aspects that need to be considered: specificity of phages, bacterial resistance, safety, immune response of the host organism, formulation, administration and stability of phage preparations as well as bacteriophages’ influence on the environment. The biggest challenge to overcome is finding the right balance between the desired and problematic characteristics of bacteriophages. Finally, regulatory approval challenges may be encountered by bacteriophage manufacturers. Even though there are still some technical constraints connected with the global use of bacteriophage therapy, it was concluded that it can be successfully applied in aquaculture.