Bacteriophages are viruses infecting bacterial cells. Since there is a lack of specific receptors for bacteriophages on eukaryotic cells, these viruses were for a long time considered to be neutral to animals and humans. However, studies of recent years provided clear evidence that bacteriophages can interact with eukaryotic cells, significantly influencing the functions of tissues, organs, and systems of mammals, including humans. In this review article, we summarize and discuss recent discoveries in the field of interactions of phages with animal and human organisms. Possibilities of penetration of bacteriophages into eukaryotic cells, tissues, and organs are discussed, and evidence of the effects of phages on functions of the immune system, respiratory system, central nervous system, gastrointestinal system, urinary tract, and reproductive system are presented and discussed. Modulations of cancer cells by bacteriophages are indicated. Direct and indirect effects of virulent and temperate phages are discussed. We conclude that interactions of bacteriophages with animal and human organisms are robust, and they must be taken under consideration when using these viruses in medicine, especially in phage therapy, and in biotechnological applications.