Bacteriophages (phages) evolve rapidly by acquiring genes from other phages leading to mosaic genomes. Here, we identify numerous genetic transfers between distantly related phages and aim at understanding their frequency, consequences and the conditions favoring them. Gene flow tends to occur between phages that are enriched for recombinases, transposases and non-homologous end joining, suggesting that both homologous and illegitimate recombination contribute to gene flow. Phage family and host phyla are strong barriers to gene exchange, but phage lifestyle is not. Even if we observe four times more recent transfers between temperate phages than between other pairs, there is extensive gene flow between temperate and virulent phages, and between the latter. These predominantly involve virulent phages with large genomes previously classed as low gene flux, and lead to the preferential transfer of genes encoding functions involved in cell energetics, nucleotide metabolism, DNA packaging and injection, and virion assembly. Such exchanges may contribute to the observed twice larger genomes of virulent phages. We used genetic transfers, which occur upon co-infection of a host, to compare phage host range. We found that virulent phages have broader host ranges and can mediate genetic exchanges between narrow host range temperate phages infecting distant bacterial hosts, thus contributing to gene flow between virulent phages, as well as between temperate phages. This gene flow drastically expands the gene repertoires available for phage and bacterial evolution, including the transfer of functional innovations across taxa.