Membrane fusion and fission are two key processes that occur during the replication of enveloped viruses, namely access to the interior of the host-cell (entry, which requires fusion of the viral envelope with the target cell envelope) and dissemination of viral progeny after replication (egress, which involves budding and fission). These dynamic processes are mediated by specialized proteins that modify and bend the lipid bilayer transiently and locally. This review focuses on fusion and fission reactions and on the hypothetical shared mechanism that generates their driving force.