A survey of experimental results on noncollinear spin structures in crystalline and amorphous ionic materials is given. The occurrence of coherent helical, triangular, and canted structures in pure crystals is related to the presence of competing interactions: topologically frustrated antiferromagnetic superexchange, positive and negative exchange coupling with different shells of neighbours, symmetric and antisymmetric exchange, or exchange and single-ion anisotropy. These ideas are extended to crystal surfaces, disordered crystals, mixed crystals, amorphous compounds, and complex multicomponent glasses. Random noncollinear structures found in all these materials are due to randomly competing interactions. A distinction is made between isotropic random structures, where spin correlations are very short-ranged in all directions, and those structures where comparatively long-range longitudinal ferro-, antiferro-, or ferrimagnetic correlations coexist with transverse spin freezing having correlations only on the scale of nearest neighbour distances. A generalized magnetic phase diagram for diluted random magnets is presented. It is emphasized that important aspects of those systems now known as "reentrant spin glasses" had already been described in diamagnetically substituted ferrites many years previously.