Magnetic measurements in the superconducting state of the high temperature superconductors have been characterized by the feature of irreversibility. Similar effects have been known in the conventional type II superconductors for about three decades now, and have been studied in great detail during the last few years. Recent studies of magnetic irreversibilities, in both conventional and high temperature superconductors, will be reviewed here. Thermally-activated relaxation accompanies such irreversibilities, and studies on flux-creep will also be reviewed. This review shall cover the measurement of isothermal magnetization curves, of ac susceptibility, of thermo-magnetic history effects in the magnetization at a particular field and temperature, and of flux creep. An understanding of these in terms of Bean's celebrated macroscopic model shall be discussed. We shall also cover measurements that confirm the existence of weak links in ceramic high-temperature, as well as in conventional multifilamentary, superconductors.