This paper examines various philosophical arguments to do with time travel. It argues that time travel has not been shown to be logically impossible. It then considers whether time travel would give rise to improbable strings of coincidences, or closed causal loops. Finally, it considers whether we could ever be justified in believing someone who claimed to be a time traveller, or whether we would always be more justified in believing that the claimant was either deluded or trying to deceive us. For this last issue the Terry Gilliam film ‘Twelve Monkeys’ is used as an example.