Supertasks and Spacetime David O'Connell Abstract: In recent years, discussions of supertasks involved a particular class of physical models known as Malament-Hogarth spacetimes. One might wonder – what is the role of physical models in the philosophical discussion of supertasks? Why Malament-Hogarth spacetimes in particular? In this paper we trace the early history of relativistic supertasks, as well as the subsequent discussions of Malament-Hogarth spacetimes as physically-reasonable models of supertasks.