The study of microstructural evolution in polycrystalline materials has been active for many decades so it is interesting to illustrate the progress that has been made and to point out some remaining challenges. Grain boundaries are important because their long-range motion controls evolution in many cases. We have some understanding of the essential features of grain boundary properties over the five macroscopic degrees of freedom. Excess free energy, for example, is dominated by the two surfaces that comprise the boundary although the twist component also has a non-negligible influence. Mobility is less well defined although there are some clear trends for certain classes of materials such as fcc metals. Computer simulation has made a critical contribution by showing, for example, that mobility exhibits an intrinsic crystallographic anisotropy even in the absence of impurities. At the mesoscopic level, we now have rigorous relationships between geometry and growth rates for individual grains in three dimensions. We are in the process of validating computer models of grain growth against 3D non-destructive measurements. Quantitative modeling of recrystallization that includes texture development has been accomplished in several groups. Other properties such as corrosion resistance are being related quantitatively to microstructure. There remain, however, numerous challenges. Despite decades of study, we still do not have complete cause-and-effect descriptions of most cases of abnormal grain growth. The response of nanostructured materials to annealing can lead to either unexpected resistance to coarsening, or, coarsening at unexpectedly low temperatures. General process models for recrystallization that can be applied to industrial alloys remain elusive although significant progress has been made for the specific case of aluminum alloy processing. Thin films often exhibit stagnation of grain growth that we do not fully understand, as well as abnormal grain growth. Grain boundaries respond to driving forces in more complicated ways than we understood. Clearly many exciting challenges remain in grain growth and recrystallization.