Persistent oncovirus infections account for 15-20% of the global cancer burden, driving multiple forms of human cancer. To maintain persistent infection and spread, oncoviruses drive alterations in host cell metabolism, immune signaling, and cell-to-cell communication throughout tumor microenvironments. Accumulating evidence has indicated that these alterations occur in conjunction with a range of organelle remodeling events that can differ between "dormant" viral latency and active lytic replication. Throughout each phase of infection, oncoviruses alter the morphology, composition, and function of organelles to promote cellular survival and proliferation, while periodically supporting viral replication. Here, we review oncovirus-driven organelle remodeling strategies across distinct infection states, including viral latency, reactivation from latency, and chronic active replication. We focus on the molecular mechanisms by which oncovirus-driven organelle remodeling promotes cellular transformation, impedes immune responses, and facilitates virion assembly and egress. We also draw parallels between remodeling strategies employed by oncogenic and oncomodulatory viruses, emphasizing broadly conserved mechanisms across cancer-associated infections. Lastly, we highlight how studies of oncovirus organelle remodeling are critical for discovering vulnerabilities in both oncogenic virus infection and viral oncogenesis, with therapeutic potential for multiple cancers.