Enveloped viruses escape infected cells by budding through limiting membranes. In the decade since the discovery that HIV recruits cellular ESCRT (endosomal sorting complexes required for transport) machinery to facilitate viral budding, this pathway has emerged as the major escape route for enveloped viruses. In cells, the ESCRT pathway catalyzes analogous membrane fission events required for the abscission stage of cytokinesis and for a series of "reverse topology" vesiculation events. Studies of enveloped virus budding are therefore providing insights into the complex cellular mechanisms of cell division and membrane protein trafficking (and vice versa). Here, we review how viruses mimic cellular recruiting signals to usurp the ESCRT pathway, discuss mechanistic models for ESCRT pathway functions, and highlight important research frontiers.