Dynamin, best studied for its role in clathrin-mediated endocytosis, is the prototypical member of a family of multidomain GTPases involved in fission and remodeling of multiple organelles. Recent studies have shown that dynamin alone can catalyze fission of membrane tubules and vesicle formation from planar lipid templates. Thus, dynamin appears to be a self-sufficient fission machine. Here we review the biochemical activities and structural features of dynamin required for fission activity. As all changes in membrane topology require energetically unfavorable rearrangements of the lipid bilayer, we discuss the interplay between dynamin and its lipid substrates that are critical to defining a nonleaky pathway to membrane fission. We propose a two-stage model for dynamin-catalyzed fission. In stage one, dynamin's mechanochemical activities induce localized curvature stress and position its lipid-interacting pleckstrin homology domains to create a catalytic center that, in stage two, guides lipid remodeling through hemifission intermediates to drive membrane fission.