Over the past 20 years or so, considerable research effort has been directed towards a better understanding of the glass transition in polymers (indeed, of amorphous materials in general), and of the associated relaxation processes, principally by the use of differential scanning calorimetry (DSC). The extent to which phenomenological approaches (e.g. 'curve fitting' and 'peak shift') can describe the response of glasses in DSC is reviewed, and the degree of enlightenment afforded by these models is discussed. More recently, the technique of temperature-modulated DSC (TMDSC), has attracted considerable attention, and its application to the glass transition of polymers is considered here within the framework of the same models as are used for conventional DSC. In particular, the two techniques of DSC and TMDSC are compared in respect of the quantitative analysis of the data and in the light of the problems of heat transfer.