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The paper concerns the mechanical performance of continuous fibre/thermosetting polymer matrix composites reinforced in the through-thickness direction with fibrous or metallic rods or threads in order to mitigate against low delamination resistance. Specific illustrations of the effects of microfasteners in reducing delamination crack growth are made for Z-pinned and tufted composites. Response to loading in such 'structured materials' is subject to multiple parameters defining their in-plane and out-of-plane properties. Single microfastener mechanical tests are well suited to establish the crack bridging laws under a range of loading modes, from simple delamination crack opening to shear, and provide the basis for predicting the corresponding response of microfastener arrays, within a given material environment. The fundamental experiments on microfasteners can be used to derive analytical expressions to describe the crack bridging behaviour in a general sense, to cover all possible loadings. These expressions can be built into cohesive element constitutive laws in a finite-element framework for modelling the effects of microfastener arrays on the out-of-plane mechanical response of reinforced structural elements, including the effects of known manufacturing imperfections. Such predictive behaviour can then be used to assess structural integrity under complex loading, as part of the component design process. This article is part of the themed issue 'Multiscale modelling of the structural integrity of composite materials'., (© 2016 The Authors.)