Persistent neural activity selective to features of an extinct stimulus has been identified as the neural correlate of working memory processes. The precise nature of the physiological substrate for this self-sustained activity is still unknown. In the last few years, this problem has gathered experimental together with computational neuroscientists in a quest to identify the cellular and network mechanisms involved. I introduce here the attractor theory framework within which current persistent activity computational models are built, and I then review the main physiological mechanisms that have been linked thereby to persistent activity and working memory. Open computational and physiological issues with these models are discussed, together with their potential experimental validation in current in vitro models of persistent activity.