Strongly periodic series occur frequently in many disciplines. This paper reviews one specific approach to analyzing such series viz. the harmonic regression approach.In this paper the five major methodsnsuggested under this approach are critically reviewed and compared, and their empirical potential highlighted via two applications. The out-of-sample forecast comparisons are made using the Superior Predictive Ability test, which specifically guards against the perils of data snooping. Certain tentative conclusions are drawn regarding the relative forecasting ability of the different methods.