Viruses exert profound evolutionary pressure on bacteria by interacting with receptors on the cell surface to initiate infection. While the majority of bacterial viruses, phages, use chromosomally-encoded cell surface structures as receptors, plasmid dependent-phages exploit plasmid-encoded conjugation proteins, making their host range dependent on horizontal transfer of the plasmid. Despite their unique biology and biotechnological significance, only a small number of plasmid-dependent phages have been characterized. Here we systematically search for new plasmid-dependent phages using a targeted discovery platform, and find that they are in fact common and abundant in nature, and vastly unexplored in terms of their genetic diversity. Plasmid-dependent tectiviruses have highly conserved genetic architecture but show profound differences in their host range which do not reflect bacterial phylogeny. Finally, we show that plasmid-dependent tectiviruses are missed by metaviromic analyses, showing the continued importance of culture-based phage discovery. Taken together, these results indicate plasmid-dependent phages play an unappreciated evolutionary role in constraining horizontal gene transfer.