Viruses are ubiquitous and the most numerous and diverse biological entities in nature. Recently, Brum and colleagues (2015) confirmed by metagenomics that "the most abundant and widespread viral population lack culture representative"in marine systems. To circumvent culture and metaviromic limitations to deliver reference genomes, we will present the usefulness of Single Virus Genomics (SVG) to unveil unknown, uncultured and ubiquitous marine viruses at global scale. We first sorted 3984 single viruses from the epipelagic zone of the Mediterranean Sea. Then, whole genome was amplified by multiple displacement amplification and sequenced single amplified viral genomes (SAVs). Metaviromic fragment recruitment with Tara Oceans expedition, Pacific Ocean Virome and Mediterranean datasets demonstrated that SAVs provided the highest recruitment rate among all publicly available marine viruses including marine virus isolates (n=180), viral fosmids (n=1149) and virus genomes assembled from TARA metaviromes (n=3018, surface) and single amplified prokaryote genomes (n=20). Most of generated SAVs were Caudovirales and unexpectedly, results indicated that the most putatively abundant virus in surface marine environment, the phage 37-F6 (mean recruitment rate over Pelagiphages ≈40-fold) was not related with Pelagiphage isolates, but the closest phages (≈55% of nucleotide identity, whole genome alignment) were those found in single cells of Verrucomicrobia (AAA164-I21) and Flavobacteria (AAA160-P02), both considered as active members of bacterioplankton (Martínez-Garcia et al., 2012). Furthermore, the analysis of a metaproteome from the Oregon Coast bacterioplankton and comparison with metaviromes confirmed that peptide signatures of structural proteins of virus 37-F6 were widespread in all oceans. Thus, overall, our results demonstrated that SVG rises as a powerful approach to unveil the genomics of uncultured viruses and open new ways to formulate and contrast hypothesis in microbial ecology, such as the predominance of virus 37-F6 and the total contribution of viruses predating on low abundant but active taxa to total viral production.