Abstract Evidence to show that the layer growth of ice crystals occurs mainly by the surface diffusion of molecules to the growing steps is presented. Measurements of the rate-of-change of separation of adjacent growth steps allow the mean migration distance x s of molecules on the basal face to be deduced; this parameter shows a remarkable variation with temperature over the range 0°C to -40°C. The six changes of ice crystal habit, which occur between 0°C and -25°C, are explained in terms of the variation of x s with temperature and the relative rates of surface diffusion on the basal and prism faces. Photographs reveal the presence of micron-size steps on the crystal surfaces and their formation is explained in terms of the bunching and amalgamation of much thinner growth layers. It is shown that if two layers are nucleated so that their initial separation is <2x s, they will close up and amalgamate to form a double step travelling at half the speed; this in turn, will be overtaken by other layers to produce eventually very slowly moving, visible steps. The rate of closing of two adjacent steps and the distance and time required for the formation of steps of a given height are calculated and found to agree quite well with observation. Hopper, skeletal and dendritic growth of ice crystals have been studied by time-lapse ciné-photography. These growth features are largely controlled by the supersaturation of the vapour. They are shown to be a consequence of nucleation of growth layers at the crystal edges and corners under high local supersaturation, unequal rates of surface diffusion on basal and prism faces, and the bunching and amalgamation of layers as they spread towards the centres of crystal faces.