Some viruses possess the remarkable ability to transport their genomes across nuclear pore complexes (NPCs) for replication inside the host cell's intact nuclear compartment. Viral mechanisms for crossing the restrictive NPC passageway are highly complex and astonishingly diverse, requiring in each case stepwise interaction between incoming virus particles and components of the nuclear transport machinery. Exactly how a large viral genome loaded with accessory proteins is able to pass through the relatively narrow central channel of the NPC without causing catastrophic structural damage is not yet fully understood. It appears likely, however, that the overall structure of the NPC changes in response to the cargo. Translocation may result in nucleic acids being misdelivered to the cytoplasm. Here we consider in detail the diverse strategies that viruses have evolved to target and subvert NPCs during infection. For decades, this process has both captivated and confounded researchers in the fields of virology, cell biology, and structural biology.