When concentrated aqueous solutions of sucrose are cooled, ice or sucrose crystals separate, depending on the concentration and temperature. The state diagram of the sucrose-water system describes both the equilibrium and non-equilibrium behaviour. A detailed account is given of the effect of sucrose concentration and various, principally polysaccharide, stabilizers on the processes of homogeneous and heterogeneous nucleation, as well as the kinetics of crystal growth. Increasing concentrations of sucrose reduce the diffusion coefficient of water molecules and the linear growth velocity of ice crystals. Polysaccharide stabilizers have relatively little effect until incipient gelation occurs. Thereafter, there is a gross change in crystal form and growth rate. A careful analysis of the impact of sucrose concentration on the rate of ice crystal growth has not permitted satisfactory matching of theoretical predictions with actual behaviour. Recent studies of the rate of growth of sucrose crystals in sucrose glasses of varying water contents are recorded. There is no simple relationship between the moisture content (in the 2-12 w/w % H2O range) and the rate of growth of the sucrose crystals.