When confronted with reminders to an unpleasant memory, people often try to prevent the unwanted memory from coming to mind. In this article, we review behavioral and neurocognitive evidence concerning the consequences of exerting such control over memory retrieval. This work indicates that suppressing retrieval is accomplished by control mechanisms that inhibit the unwanted memories, making them harder to recall later, even when desired. This process engages executive control mechanisms mediated by the lateral prefrontal cortex to terminate recollection-related activity in the hippocampus. Together, these findings specify a neurocognitive model of how memory control operates, suggesting that executive control may be an important means of down-regulating intrusive memories over time. We conclude by proposing that individual differences in the regulation of intrusive memories in the aftermath of trauma may be mediated by pre-existing differences in executive control ability. In support of this executive deficit hypothesis, we review the recent work indicating links between executive control ability and memory suppression.