It is well known that, all things being equal, the accuracy ofmammalian timing and memory decays gradually with the pas-sage of time. The gradual decay of temporal accuracy is alsoobserved in single-unit neural recordings. Here we review re-cent modeling work describing a specific mechanism for tim-ing and memory and relevant neural data. The model describesa neural mechanism that can give rise to a logarithmically com-pressed representation of the recent past. We examine the spe-cific predictions of the model, in particular that the elapse oftime is represented by sequentially activated cells which firefor a circumscribed period of time. Such cells, called timecells, have been observed in neural recordings from severalbrain regions in multiple species. As predicted by the model,the cells show accuracy that decreases with time.