The solid and liquid particles which constitute polar stratospheric clouds (PSCs) are of manifold importance to the meteorology of the stratosphere. The heterogeneous reactions which take place on and within these particles release halogens from relatively inert reservoir species into forms which can destroy ozone in the polar spring. In addition, solid PSC particles are instrumental in the physical removal of nitrogen oxides (denitrification) and water (dehydration) of regions of the polar stratosphere. Denitrification, in particular, allows extended ozone destruction by slowing the conversion of chlorine radicals back into reservoir species. We review the historical development of PSC studies, with particular emphasis on results from the last decade, encompassing developments in observations, in laboratory experiments, and in theoretical treatments. The technical challenge of measuring sufficient of the parameters describing any given polar stratospheric cloud, to allow its microphysics to be understood, has driven forward balloon-borne, aircraft, and satellite instrumentation. The technical challenge of finding suitable laboratory proxies for PSCs, in order to observe the microphysics under controlled conditions, has resulted in a wide variety of experimental designs, some of which maximise the probability of observing phase change, others of which mimic the surface-volume ratios of PSCs more closely. The challenge to theory presented by PSCs has resulted in improvements in the thermodynamics of concentrated inorganic solutions of volatile compounds, and a new general theory of freezing of water ice from concentrated aqueous solutions. Of the major processes involving PSCs, heterogeneous reaction probabilities for ternary HNO3/H2SO4/H2O solutions, and heterogeneous freezing to produce nitric acid hydrates, are the least well understood.