Misremembering is a systematic and ordinary occurrence in our daily lives. Since it is commonly assumed that the function of memory is to remember the past, misremembering is typically thought to happen because our memory system malfunctions. In this paper I argue that not all cases of misremembering are due to failures in our memory system. In particular, I argue that many ordinary cases of misremembering should not be seen as instances of memory's malfunction, but rather as the normal result of a larger cognitive system that performs a different function, and for which remembering is just one operation. Building upon extant psychological and neuroscientific evidence, I offer a picture of memory as an integral part of a larger system that supports not only thinking of what was the case and what potentially could be the case, but also what could have been the case. More precisely, I claim that remembering is a particular operation of a cognitive system that permits the flexible recombination of different components of encoded traces into representations of possible past events that might or might not have occurred, in the service of constructing mental simulations of possible future events.