Dreaming has often been viewed as a “mysterious” experience entirely distinct from waking cognition. An alternative view proposes that dreams are generated by the same fundamental processes that give rise to spontaneous thought during wakefulness. New evidence suggests that these processes include activity of the brain’s memory systems, supporting consolidation of newly encoded experience. During both sleep and wakefulness, fragments of recently encoded memory are recombined with related remote memory and semantic information to create novel scenarios. This is an adaptive process that contributes to the “consolidation” of memory and is reflected in the phenomenology of both our nightly dreams and waking daydreams.