Vast and diverse microbial communities (the microbiome) are distinct at different human body sites and strongly influence health and disease. Specifically, the respiratory tract microbiome is thought to influence outcomes after lung transplantation, the only therapeutic option for end-stage lung diseases. Studies dissecting the role of the microbiome on pulmonary health should also include the viral microbiome (virome), which is less-studied due to unique challenges in identifying these small, diverse, self-replicating genetic elements. Organ transplantation is accompanied by immunosuppression, which can result in reactivation of latent viruses, transfer of viruses from organ donor to recipient, and increased susceptibility to viral infections. We therefore used high-throughput metagenomic approaches to study the virome of lung transplant recipients (LTRs). We first characterized the virome in LTRs and its relationship to clinically defined adverse events. We discovered that a family of eukaryotic viruses (Anelloviridae) is abundant in the lung and blood of LTRs and that their levels in the lungs were associated with primary graft dysfunction, a form of acute lung injury. Next, we investigated the temporal and spatial dynamics of the virome during lung transplantation and identified herpesviruses, parvoviruses, polyomaviruses, bacteriophage and complex anellovirus populations. We focused on the abundant anelloviruses by assembling genomes from shotgun metagenomic sequences and tracking their representation in the lung and blood of LTRs post-transplantation using a metric that accounts for inter-and intra-subject viral diversity. This analysis revealed that anellovirus populations move between lung allografts and the peripheral blood of LTRs. However, many uncharacterized sequences still existed in the metagenomic data generated in these studies. To address this, we developed a molecular and bioinformatics pipeline to mine public datasets and discovered a novel family of small, circular DNA viruses (Redondoviridae). Quantification of redondoviruses in human oro-respiratory samples showed an association with periodontal disease and acute illness. Overall, this work helps define the virome during lung transplantation and introduces a new family of human viruses, broadly demonstrating the importance of exploring the human virome.