The strength of polycrystalline specimens can be related to interaction phenomena taking place during elastic and plastic deformation. Such phenomena are reviewed in term of macroscopic and microscopic strain accommodation processes required to maintain strain continuity across the grain boundaries. The strength-grain size relationships can be described in a number of empirical equations relating the yield stress and the flow stress in tension to various structural parameters. A number of such equations are reviewed and their predictive capability is discussed. Structural information of importance for the understanding of polycrystalline strengthening is obtained mainly from surface relief patterns and from bulk structures observed by transmission electron microscopy of thin foils. The results obtained by these methods are discussed and correlations are proposed. A number of features characterizing the deformed structure are summarized and the behavior of a number of metals and alloys is reviewed with emphasis on the structural changes in the interior of the grains and in the vicinity of the grain boundaries. The models for strain accommodation during deformation are discussed on the basis of the microstructures found, and this structural information is correlated with a number of strength structural equations. Finally, the flow stress of fcc and bcc polycrystalline specimens is related to the occurrence of microstructures formed by macroscopic and microscopic strain accommodation processes during plastic straining, and it is concluded that macroscopic processes may be strength determining at larger strains whereas microscopic effects may be of importance at small strains.