Many attempts have been made to localize the physical trace of a memory, or engram, in the brain. However, until recently, engrams have remained largely elusive. In this Review, we develop four defining criteria that enable us to critically assess the recent progress that has been made towards finding the engram. Recent 'capture' studies use novel approaches to tag populations of neurons that are active during memory encoding, thereby allowing these engram-associated neurons to be manipulated at later times. We propose that findings from these capture studies represent considerable progress in allowing us to observe, erase and express the engram.