The results of experimental studies on hysteresis in magnetization, thermomagnetic history effects, anomalous variations in magnetic hysteresis curves and the decay rates of magnetization obtained under different thermomagnetic histories in specimens of conventional and high temperature superconductors are presented. The Bean’s critical state model is considered adequate to explain magnetic behaviour in conventional hard superconductors. The similarity in the general features of the results of different experiments on specimens of the two families of superconductors underscores the efficacy of the said model to understand some aspects of the macroscopic magnetic response of high temperature superconductors as well. For instance, the isothermal magnetization hysteresis loop which comprises of magnetization curves along forward (−H_max to +H_max) and reverse (+H_max to −H_max) paths define an envelop within which all isothermal magnetization data along different thermomagnetic histories lie. There exist inequality relationship between various field values identified asH_peak,H_I,H_II etc. in isothermal magnetization hysteresis as well as magnetic relaxation data. The entire field span of an isothermal magnetization hysteresis data set can be considered to comprise of three parts corresponding to (M_rem(H)−M_FC(H)+M_ZFC(H)) being equal to, less than or greater than zero, whereM_rem(H) are the remanent magnetization values obtained on reducing field to zero after having the specimen in different applied field (H) values. There are, however some situations amongst thermomagnetic history effects in specimens which show incomplete flux trapping on field cooling, where the critical state model has been found inadequate.