Phages are extremely abundant in the oceans, influencing the population dynamics, diversity and evolution of their hosts. Here we assessed the diversity and phylogenetic relationships among T7-like cyanophages using DNA polymerase (replication), major capsid (structural) and photosynthesis psbA (host-derived) genes from isolated phages. DNA polymerase and major capsid phylogeny divided them into two discrete clades with no evidence for gene exchange between clades. Clade A phages primarily infect Synechococcus while clade B phages infect either Synechococcus or Prochlorococcus. The major capsid gene of one of the phages from clade B carries a putative intron. Nearly all clade B phages encode psbA whereas clade A phages do not. This suggests an ancient separation between cyanophages from these two clades, with the acquisition or loss of psbA occurring around the time of their divergence. A mix and match of clustering patterns was found for the replication and structural genes within each major clade, even among phages infecting different host genera. This is suggestive of numerous gene exchanges within each major clade and indicates that core phage functions have not coevolved with specific hosts. In contrast, clustering of phage psbA broadly tracks that of the host genus. These findings suggest that T7-like cyanophages evolve through clade-limited gene exchanges and that different genes are subjected to vastly different selection pressures.