The regularities of the formation and structure of plastic and damage zones in structural materials of different types are considered. Our own experimental investigations of the plastic zone structure in metals and extensive literature data analysis are used as the basis for identifying general and particular features of the development of localised damage zones in various materials and at various length scales differing by several orders of magnitude. A single zone of severe deformation (the fracture process zone) is formed at the tip of a crack or a notch in a material in the brittle state. We show that the process of fracture in ductile and quasibrittle materials is accompanied by the formation of at least of two localised zones characterised by different degrees of deformation and damage: the inner fracture process zone (FPZ) of severe deformation, and the outer, plastic zone (PZ) or damage zone (DZ) where the degree of damage or deformation is lower. It is the presence of the outer zone of moderate deformation and damage (PZ or DZ) that gives rise to the appearance of the size effect. We consider the structure of crack tip zones (FPZ, and PZ or DZ) in materials other than metals, namely, in rubber toughened polymers, concrete, and rocks. We discuss that the fracture properties of different materials are determined by the mechanisms of damage accumulation in the crack tip zones and by the transition from low constraint (plane stress) to high constraint (plane strain) conditions near the crack tip. Although the mechanisms of damage accumulation in different materials may differ, we suggest that in all cases the disappearance of the outer zone (and hence the lack of size effect on strength) is a consequence of the presence of material hardening (as opposed to softening).