Geometrical frustration covers situations where a certain type of local order, favoured by physical interactions, cannot propagate throughout space. A classical example is that of pentagonal, or icosahedral, order which appears in the three-dimensional sphere packing problem. This symmetry, which is not compatible with translations, is nevertheless met, often imperfectly, in numerous materials. Such strong contradictions between local and global configurations are found in various physical systems, with different kinds of interactions, and coherence sizes. The concept of frustration then applies to metallic alloys at the atomic scale, to liquid crystal organizations like amphiphiles films or cholesteric blue phases at the scale of hundreds of thousands of ångströms, and even to larger scales with some biological structures.