For 25 years, theory about the causes of, and possible solutions to, the problem of unemployment has been dominated by Phelps' and Friedman's natural rate of unemployment hypothesis. This postulates that the equilibrium rate of unemployment consistent with steady inflation is determined by structural variables: sustainable reductions in unemployment can be achieved only by measures to change underlying microeconomic structures, such as benefit and pay bargaining systems. Belief in the hypothesis has faltered since the 1980s, the hypothesis being unable to explain the dramatic upward shifts in European unemployment rates. These essays reflect upon the fundamental structures underlying the hypothesis, assess the related evidence, and look forwards, suggesting possible modifications. In contrast to the single rate postulated by the natural rate hypothesis, several of the contributors propose that there are ranges of unemployment rates consistent with steady inflation.