Shear flow changes the equilibrium state of systems. In one case, the increased shear rate brings about shear-induced two-phase to single-phase transition, whereas in the other case, it brings about shear-induced single-phase to two-phase transitionShear-induced single-phase to two-phase transition. The former and latter occur in dynamically symmetric systemsDynamically symmetric systems and dynamically asymmetric systemsDynamically asymmetric system, respectively. In dynamically symmetric mixtures, component molecules A and B have equal mobility, whereas in dynamically asymmetric mixtures, component molecules have different mobilities as in the case of mixtures of polymers having different self-diffusivities. The thermally built-up local concentration fluctuations generally build up local stress and its stress relaxation with time, which affects the free energy of the system. In the dynamically symmetric systemsDynamically symmetric systems, this stress is equally divided into the two components, and the stress relaxation rate is faster than the growth rate of the concentration fluctuations. Thereby, the stress built-up and its relaxation give no influence on the structural growth. On the other hand, in the dynamically asymmetric systemsDynamically asymmetric system, the stress born by the fast component relaxes faster than the stress born by its counterpart, so that the local stress is primarily born by the smaller mobility component. This local stress and the stress relaxation affect the free energy functional and hence the cooperative diffusivity of the slower mobility component of the systems. This stress-diffusion couplingStress-diffusion coupling inherent to the asymmetric systems gives rise to intriguing effects on the dynamics of the composition fluctuations and pattern formation. The chapter describes some general backgrounds on self-organization of dynamically symmetric and asymmetric systems under shear flow.