This chapter examines the logical, metaphysical, and physical possibility of time travel understood in the sense of the existence of closed worldlines that can be traced out by physical objects, arguing that none of the purported paradoxes rule out time travel on the grounds of either logic or metaphysics. More relevantly, modern space–time theories such as general relativity seem to permit models that feature closed worldlines. The chapter discusses what this apparent physical possibility of time travel means, and, furthermore, reviews the recent literature on so-called time machines, of devices that produce closed worldlines where none would have existed otherwise. Finally, it investigates what the implications of the quantum behavior of matter might be for the possibility of time travel, and explicates in what sense time travel might be possible according to leading contenders for full quantum theories of gravity such as string theory and loop quantum gravity.