The concrete industry is facing new digital shaping processes that still have to be optimized and that require cement-based materials, for which fresh properties requirements are yet to be defined. In this paper, we first present the state of the art in the field of numerical simulations of concrete flow. We then focus on the literature on numerical simulations of extrusion-based additive manufacturing processes for concrete. Our review shows that the available numerical modelling tools are able to detect and predict various type of failures through the printing process, no matter if these happen at the scale of the nozzle, of one printed layer or of the entire object being printed. As they allow for a systematic evaluation of the influence of the entire range of material, geometric and process parameters, numerical modelling is a valid option to optimize both process and material.