In the present contribution, the capabilities of classical and higher order damage-plasticity continuum models in their ability to predict complex shear failure of concrete is assessed. To this end, a classical local formulation of the popular Concrete Damage-Plasticity model by Grassl and Jirásek (2006a) with mesh-adjusted softening modulus is compared to a higher order gradient-enhanced formulation by Poh and Swaddiwudhipong (2009) and a recently proposed gradient-enhanced micropolar formulation by Neuner et al. (2020a) by means of challenging 3D finite element simulations of a transverse shear test. The transverse shear test is characterized by an anchor channel embedded in a concrete slab, which is loaded transversely to its axis until failure. A comparison with experimental results highlights the limitations of classical local formulations, whereas higher order continuum approaches show great potential in particular for modeling the structural post-peak response.