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Concrete is the most widely used man made material in the world. Reinforced with steel, it forms a key enabler behind our rapidly urbanising built environment. Yet despite its ubiquity, the failure behaviour of the material in shear is still not well understood. Many different shear models have been proposed over the years, often validated against sets of physical tests, but none of these has yet been shown to be sufficiently general to account for the behaviour of all possible types and geometries of reinforced concrete structures. A key barrier to a general model is that concrete must crack in tension, and in shear such cracks form rapidly to create brittle failure. Peridynamics (PD) is a non-local theory where the continuum mechanics equilibrium equation is reformulated in an integral form, thereby permitting discontinuities to arise naturally from the formulation. On the one hand, this offers the potential to provide a general concrete model. On the other hand, PD models for concrete structures have not focussed on applications with reinforcement. Moreover, a robust model validation that assesses the strengths and weakness of a given model is missing. The objectives of this paper are twofold: (1) to evaluate the benchmark tests involving shear failure for RC structures; and (2) to review the most recent PD theory and its application for reinforced concrete (RC) structures. We investigate these models in detail and propose benchmark tests that a PD model should be able to simulate accurately.