We use molecular dynamics simulations to study phase separation of a 50:50 (by volume) fluid mixture in a confined and curved (Taylor–Couette) geometry, consisting of two concentric cylinders. The inner cylinder may be rotated to achieve a shear flow. In nonsheared systems we observe that, for all cases under consideration, the final equilibrium state has a stacked structure. Depending on the lowest free energy in the geometry the stack may be either flat, with its normal in the z direction, or curved, with its normal in the r or direction. In sheared systems we make several observations. First, when starting from a prearranged stacked structure, we find that sheared gradient and vorticity stacks retain their character for the durations of the simulation, even when another configuration is preferred (as found when starting from a randomly mixed configuration). This slow transition to another configuration is attributed to a large free energy barrier between the two states. In case of stacks with a normal in the gradient direction, we find interesting interfacial waves moving with a prescribed angular velocity in the flow direction. Because such a wave is not observed in simulations with a flat geometry at similar shear rates, the curvature of the wall is an essential ingredient of this phenomenon. Second, when starting from a randomly mixed configuration, stacks are also observed, with an orientation that depends on the applied shear rate. Such transitions to other orientations are similar to observations in microphase separated diblock copolymer melts. At higher shear rates complex patterns emerge, accompanied by deviations from a homogeneous flow profile. The transition from steady stacks to complex patterns takes place around a shear rate 1/dv, where dv is the crossover time from diffusive to viscous dominated growth of phase-separated domains, as measured in equilibrium simulations.