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Abstract Many two-phase alloys work-harden much faster than do pure single crystals. This is because the two phases are not equally easy to deform. One component (often dispersed as small particles) deforms less than the other, or not at all, so that gradients of deformation form with a wavelength equal to the spacing between the phases or particles. Such alloys are 'plastically non-homogeneous', because gradients of plastic deformation are imposed by the microstructure. Dislocations are stored in them to accommodate the deformation gradients, and so allow compatible deformation of the two phases. We call these 'geometrically-necessary' dislocations to distinguish them from the 'statistically-stored' dislocations which accumulate in pure crystals during straining and are responsible for the normal 3-stage hardening. Polycrystals of pure metals are also plastically non-homogeneous. The density and arrangement of the geometrically-necessary dislocations can be calculated fairly exactly and checked by electron microscopy and x-ray techniques. The rate at which they accumulate with strain is conveniently described by the 'geometric slip distance', a characteristic of the microstructure. Their arrangement is quite different from that of the statistically-stored dislocations, which may make them particularly susceptible to recovery effects, even at low temperatures. Geometrically-necessary dislocations control the work hardening of the specimen when their density exceeds that of the statistically-stored ones. They contribute to hardening in two ways: by acting as individual obstacles to slip, and (collectively) by creating a long-range back-stress, with wave-length equal to the particle spacing. With the exception of single-phase single crystals, almost all metals and alloys are plastically non-homogeneous to some extent. The model provides an explanation for the way in which the stress-strain curve is influenced by a dispersion of particles, and by grain size.