Normal grain growth is the coarsening of the microstructure of polycrystalline materials via the migration of grain boundaries (GBs). It is driven by capillarity, the tendency of the microstructure to decrease the free energy of the system i.e., the product of the GB energy/area and the area of the GBs in the microstructure. The classical description of this problem, introduced over a half-century ago, is that this is GB mean curvature flow. Most theories of grain growth, going back to von Neumann and Mullins, are based on this description. A number of recent experimental observations have shown that this description is an over idealization of what happens during grain growth. The failure of the mean curvature flow ansatz may be traced to the facts that grains are solid, crystalline materials (capable of carrying mechanical loads). Crystallinity implies that GB migration occurs through the motion of disconnections (line defects constrained to GBs that have both step and dislocation character). GB migration and GB sliding occur in a fixed ratio determined by the relative orientations of the two grains delimiting the GB; this is shear coupling. Hence, grain growth leads to internal stress generation (associated with shear coupling). Internal stresses from one (part of a) GB affect the motion of other (parts of a) GB through a Peach-Koehler force and thereby modify grain growth. In this presentation, we review our recent continuum model of GB migration, based on a disconnection density description, and its implementation in a phase field method. We apply this computational approach to grain growth (including capillarity, internal and applied stresses). We demonstrate how microstructure evolution that includes internal stress generation leads to microstructure evolution that differs in profound ways from mean curvature flow grain growth; steady-state grain size distribution, topology distribution, grain aspect ratios, … We also perform statistical analysis of microstructural evolution in our shear coupled model with recent experimental and molecular dynamics simulation results on three different polycrystalline systems. The agreement is remarkable and in clear distinction with curvature flow simulation-based results. We discuss future developments for quantitative microstructure evolution.