The human virome, comprising eukaryotic viruses, bacteriophages, and viral genetic material, is a dynamic component of the microbiome with growing relevance in infectious diseases. This narrative review is structured to: (i) summarize the general composition of the human virome and methodological challenges, including the fraction of unclassified viral “dark matter”; (ii) describe virome alterations in chronic infections; and (iii) explore site-specific virome dynamics across respiratory, intestinal, and genito-urinary tracts in both chronic and acute infections. In chronic viral infections such as HIV, HBV, HCV, and HPV, a recurrent feature is the expansion of Anelloviridae—particularly torque teno virus—reflecting impaired immune surveillance rather than direct pathogenicity, suggesting their potential as surrogate biomarkers of immune competence. Evidence on virome changes in chronic bacterial and parasitic infections remains limited, highlighting a critical knowledge gap. Acute infections are associated with compartment-specific shifts in eukaryotic viruses and bacteriophage communities, often paralleling changes in bacterial populations and inflammatory responses, with implications for disease severity. Despite advances in metagenomic approaches, a substantial proportion of viral sequences remains unclassified, limiting functional interpretation. Nevertheless, virome profiling provides an ecosystem-level perspective, offering insights beyond single-pathogen detection and supporting emerging applications in diagnostics, immune monitoring, prognosis, and infectious disease surveillance.