When a mixture of large and small grains flows under gravity, the grains may segregate, with the large ones typically rising to the surface. Segregation of size-bidisperse mixtures has been studied extensively for size ratios of three or less, but comparatively little is known about segregation of grains with more widely varying sizes, despite their relevance to natural and industrial flows. At larger size ratios, the segregation behaviour may change drastically, including reversal of the direction of segregation. In this talk, we investigate the segregation behaviour of bidisperse granular mixtures up to a size ratio of seven and formulate a new continuum model for size segregation that captures the observed suppression and reversal of segregation. We also present a striking layering effect, in which the large grains self-organise into layers one grain thick, separated by thin bands of small grains. Numerical simulations reveal the structure of this layering and it is demonstrated, for the first time, in laboratory experiments.