An important challenge for memory is the competition between appropriate and inappropriate information during retrieval. This competition is normally reduced thanks to controlled inhibitory processes that suppress irrelevant memories. In Alzheimer's disease (AD), compromise of suppression ability may result in strong competition between relevant and irrelevant memories during retrieval. The present review highlights this issue by examining studies using the directed forgetting method in AD. This method in which participants are typically instructed to forget no longer relevant information is argued to reflect suppression in memory. Studies using the directed forgetting method suggest that AD participants experience difficulties when they are asked to suppress no longer relevant information in working, autobiographical, source and destination memory. Difficulties in suppressing irrelevant information, as may be observed in AD, may hamper memory retrieval by activating irrelevant memories at the expense of relevant ones.