Recent advances in game theory have made it possible to study monetary policy credibility in a more structured fashion. Some have used these new models to argue that there is less need to place legal restraints on monetary policy than was previously believed; reputational considerations discourage the monetary authorities from attempting surprise inflations. In this study, I critically assess a number of alternative models of monetary policy reputation, including some variants which have not been examined previously. The bulk of the paper is concerned with comparing specific details of these models. One general conclusion is that although the first generation of models of monetary policy reputation yield a significant number of important insights, it is premature to argue that time consistency is not a major issue in the design of monetary policy institutions. The main problem is that the models either yield a multiplicity of equilibria, or/and yield conclusions which are very sensitive to apparently minor changes in the information structure. Whereas an optimal reputational equilibrium can be achieved without any explicit cooperation among atomistic private agents, it is not (yet) clear how they coordinate on expectations strategies.