Conventional memory theory proposes that the hippocampus is initially responsible for encoding new information, before this responsibility is gradually transferred to the neocortex. Therefore, a report in 2011 by Sharon et al. of hippocampal-independent learning in humans was notable. These authors reported normal learning of new object-name associations under a Fast Mapping (FM) procedure in adults with hippocampal damage, who were amnesic according to more conventional explicit memorisation procedures. FM is an incidental learning paradigm, inspired by vocabulary acquisition in children, which is hypothesised to allow rapid, cortical-based memory formation. In the years since the original report, there has been, understandably, a growing interest in adult FM, not only because of its theoretical importance, but also because of its potential to help rehabilitate individuals with memory problems. We review the FM literature in individuals with amnesia and in healthy adults, using both explicit and implicit memory measures. Contrary to other recent reviews, we conclude that the evidence for FM in adults is weak, and restraint is needed before assuming the phenomenon exists.