Ever since Plato proposed that memories are analogous to impressions in wax, many have suggested that memories are formed through the creation of traces, representations of the things remembered. That is still the received view among most cognitive scientists, who believe the remaining challenge is simply to determine the precise physical nature of memory traces. However, there are compelling reasons for thinking that this standard view of memory is profoundly wrongheaded — in fact, disguised nonsense. This paper considers, firstly, what those reasons are in detail. Secondly and more briefly, it considers how trace-like constructs have undermined various areas of parapsychological theorizing, especially in connection with the evidence for postmortem survival — for example, speculations about cellular memory in transplant cases and genetic memory in reincarnation cases. Similar problems also emerge in areas often related to parapsychology — for example, Sheldrake’s (1981) account of morphic resonance.