Viral primary infections and reactivations are common complications in patients after solid organ transplantation (SOT) and hematopoietic stem cell transplantation (HSCT) and are associated with high morbidity and mortality. Among these patients, viral infections are frequently associated with viremia. Beyond the usual well-known viruses that are part of the routine clinical management of transplant recipients, numerous other viral signatures or genomes can be identified in the blood of these patients. The identification of novel viral species and variants by metagenomic next-generation sequencing has opened up a new field of investigation and new paradigms. Thus, there is a need to thoroughly describe the state of knowledge in this field with a review of all viral infections that should be scrutinized in high-risk populations. Here, we review the eukaryotic DNA and RNA viruses identified in blood, plasma, or serum samples of pediatric and adult SOT/HSCT recipients and the prevalence of their detection, with a particular focus on recently identified viruses and those for which their potential association with disease remains to be investigated, such as members of the Polyomaviridae, Anelloviridae, Flaviviridae, and Astroviridae families. Current knowledge of the clinical significance of these viral infections with associated viremia among transplant recipients is also discussed. To ensure a comprehensive description in these two populations, individuals described as healthy (mostly blood donors) are considered for comparative purposes. The list of viruses that should be on the clinicians' radar is certainly incomplete and will expand, but the challenge is to identify those of possible clinical significance.