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The Schmid law, which is accurate for face-centered-cubic (fcc) metals, assumes that only the shear stress acting in the slip plane in the slip direction controls the plastic deformation. Hence, it is implicitly assumed that the critical resolved shear stress (CRSS) for the slip is not affected by any other components of the applied stress tensor. This rule is almost ubiquitously utilized in large-scale continuum computations of plastically deforming single and polycrystals. On the other hand, in materials with more complex structures and for some orientations of the dislocation line the cores can spread onto several non-parallel planes. The most widely-known example is the screw dislocation in bcc metals, though this phenomenon is quite universal in structures that are not close packed. Signatures of such core configurations commonly include unexpected deformation modes and slip geometries, strong and unusual dependence of flow stresses on temperature and strain rate, a high Peierls stress, and, in general, a breakdown of the Schmid law. In this paper, we first summarize results of atomistic computer simulations of the response of 1/2 1 1 1 screw dislocations to the applied shear stresses. The calculations have been made using central-force many-body potentials and tight-binding based bond-order potentials for molybdenum. While the core structure found is not the same for the two descriptions of atomic interactions, both lead to a very similar orientation dependence of the critical resolved shear stress for the dislocation motion which takes place along the most highly stressed {1 1 0} plane. This dependence reveals the break down of the Schmid law invoked by the effect of shear stresses acting in another {1 1 0} plane, which are called non-glide stresses. These results are then transferred to macroscopic level by formulating single crystal yield criteria that include the effects of non-glide components of the stress tensor. These criteria form a basis for multislip yield criteria and flow relations for continuum analyses. Using this approach we demonstrate that the effects of non-glide stresses that have their origin at the level of individual dislocations also have significant effect on polycrystalline response, including a significant tension-compression asymmetry.