This chapter investigates the metaphysical problem of persistence, that is the way in which entities exist and continue to exist at different instants of time. We take into account three major theories: endurantism (more akin to common sense), which posits that objects are wholly present at every moment of time; perdurantism, which views objects as four-dimensional entities constituted not only by spatial parts but also by temporal parts; and exdurantism (or stage theory), which considers objects persisting in time as series of instantaneous stages. It also explores the theoretical intertwining between these views with the most important metaphysical theories of time like presentism and eternalism. Some combinations of views turn out to be more natural than others. Finally, the chapter addresses the ancient metaphysical problem of becoming and change. In particular, it provides an analysis of the metaphysical structure of future events as they become present and then past, as well as the qualitative transformation of an object that acquires and loses certain properties.