Phages exert profound evolutionary pressure on bacteria by interacting with receptors on the cell surface to initiate infection. While the majority of 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 targeting IncP and IncF plasmids using a targeted discovery platform, and find that they are common and abundant in wastewater, and largely unexplored in terms of their genetic diversity. Plasmid-dependent phages are enriched in non-canonical types of phages, and all but one of the 64 phages we isolated were non-tailed, and members of the lipid-containing tectiviruses, ssDNA filamentous phages or ssRNA phages. We show that plasmid-dependent tectiviruses exhibit profound differences in their host range which is associated with variation in the phage holin protein. Despite their relatively high abundance in wastewater, plasmid-dependent tectiviruses are missed by metaviromic analyses, underscoring the continued importance of culture-based phage discovery. Finally, we identify a tailed phage dependent on the IncF plasmid, and find related structural genes in phages that use the orthogonal type 4 pilus as a receptor, highlighting the promiscuous use of these distinct contractile structures by multiple groups of phages. Taken together, these results indicate plasmid-dependent phages play an under-appreciated evolutionary role in constraining horizontal gene transfer via conjugative plasmids.