An enduring problem in neuroscience is determining whether cases of amnesia result from eradication of the memory trace (storage impairment) or if the trace is present but inaccessible (retrieval impairment). The most direct approach to resolving this question is to quantify changes in the brain mechanisms of long-term memory (BM-LTM). This approach argues that if the amnesia is due to a retrieval failure, BM-LTM should remain at levels comparable to trained, unimpaired animals. Conversely, if memories are erased, BM-LTM should be reduced to resemble untrained levels. Here we review the use of BM-LTM in a number of studies that induced amnesia by targeting memory maintenance or reconsolidation. The literature strongly suggests that such amnesia is due to storage rather than retrieval impairments. We also describe the shortcomings of the purely behavioral protocol that purports to show recovery from amnesia as a method of understanding the nature of amnesia. Expected final online publication date for the Annual Review of Neuroscience, Volume 43 is July 8, 2020. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.