We outline a dual systems approach to temporal cognition, which distinguishes between two cognitive systems for dealing with how things unfold over time – a temporal updating system and a temporal reasoning system – of which the former is both phylogenetically and ontogenetically more primitive than the latter, and which are at work alongside each other in adult human cognition. We describe the main features of each of the two systems, the types of behavior the more primitive temporal updating system can support, and the respects in which it is more limited than the temporal reasoning system. We then use the distinction between the two systems to interpret findings in comparative and developmental psychology, arguing that animals operate only with a temporal updating system and that children start out doing so too, before gradually becoming capable of thinking and reasoning about time. After this, we turn to adult human cognition and suggest that our account can also shed light on a specific feature of our everyday thinking about time that has been the subject of debate in the philosophy of time, which consists in a tendency to think about the nature of time itself in a way that appears ultimately self-contradictory. We conclude by considering the topic of intertemporal choice, and argue that drawing the distinction between temporal updating and temporal reasoning is also useful in the context of characterising two distinct mechanisms for delaying gratification.