A step-shear deformation imparts an instantaneous, anisotropic stimulus onto a microphase-separated block copolymer mesophase. In response to the concomitant molecular stretching and collective deformation of the morphology, the system relaxes toward a long-lived, pseudometastable state with a minuscule residual shear stress. Using molecular simulations and self-consistent field theory (SCFT) calculations, we systematically explore the variety of ordered, anisotropic mesostructures that have potential applications in engineering functional materials and can be fabricated by this versatile processing strategy. We study three classes of anisotropic ordered mesostructures, including cylindroids, gyroid-like networks, and sloping lamellae, and show that their domain shape and domain orientation can be independently controlled by the magnitude of the step-shear strain, gamma, and the composition of the block copolymer as well as by the way in which we implement the step-shear deformation. We also demonstrate that pseudometastability requires a positive curvature of the free energy F(gamma) as a function of the step-shear strain. Otherwise, for d(2)F/d gamma(2) < 0, the mesostructure spontaneously relaxes back at fixed strain, and we study this relaxation via slippage by dynamic self-consistent field theory (DSCFT).