The human gut contains a vast array of viruses, mostly bacteriophages. The majority remain uncharacterized, and their roles in shaping the gut microbiome and in impacting on human health remain poorly understood. We performed longitudinal metagenomic analysis of fecal viruses in healthy adults that reveal high temporal stability, individual specificity, and correlation with the bacterial microbiome. Using a database-independent approach that uses most of the sequencing data, we uncovered the existence of a stable, numerically predominant individual-specific persistent personal virome. Clustering of viral genomes and de novo taxonomic annotation identified several groups of crAss-like and Microviridae bacteriophages as the most stable colonizers of the human gut. CRISPR-based host prediction highlighted connections between these stable viral communities and highly predominant gut bacterial taxa such as Bacteroides, Prevotella, and Faecalibacterium. This study provides insights into the structure of the human gut virome and serves as an important baseline for hypothesis-driven research. Display omitted •The human gut virome is highly individual and stable for up to 1 year•A stable and predominant fraction of viruses constitutes a persistent personal virome•Persistent bacteriophages can be linked to highly predominant gut bacterial taxa•Virulent crAss-like and Microviridae bacteriophages predominate and persist in the gut Shkoporov et al. demonstrate high individual specificity and temporal stability of the human gut virome. They describe a numerically prevalent and persisting fraction of the viral community, termed persistent personal virome (PPV). The PPV consists mainly of virulent bacteriophages predicted to target major taxonomic groups of gut bacteria.