This paper argues that the natural rate of unemployment hypothesis, in which equilibrium unemployment is determined by ‘structural’ variables alone, is wrong: it is both implausible and inconsistent with the evidence. Instead, equilibrium unemployment is haunted by hysteresis. The curious history of the natural rate hypothesis is considered, curious because the authors of the hypothesis thought hysteresis to be relevant. The various methods that have been used to model hysteresis in economic systems are outlined, including the Preisach model with its selective, erasable memory properties. The evidence regarding hysteresis effects on output and unemployment is then reviewed.