We provide an overview of our research on sheet flows and avalanches of granular materials, primarily in terrestrial conditions. Sheet flows are relatively thin, highly concentrated regions of grains that flow near the ground under the influence of a strong turbulent wind. In them grains are suspended by interparticle collisions and the velocity fluctuations of the turbulent gas. Avalanches are flows of dry, cohesionless granular materials that are driven by gravity down inclines against the frictional and collisional resistance of the grains of the bed. In our study of sheet flows, we have extended existing theories that involve particle-particle and gas-particle interactions to apply to the conditions of a typical terrestrial sand dune during a sandstorm. This has involved the incorporation of both the viscous dissipation of the particle fluctuation energy due to the gas and the turbulent suspension of the grains due to velocity fluctuations of the gas. It has also involved an examination of several different boundary conditions at the bed and a more precise characterization of the conditions that apply at the top of a sheet flow, where the mean-free-path between collisions becomes comparable to the length of a ballistic trajectory. Solutions to the resulting differential equations have been obtained for both steady and unsteady fully-developed flow. The latter solutions provide information on the characteristic time to achieve a steady flow that plays a key role in dune formation. In support of this modeling effort, experiments have been undertaken to provide a better understanding of the interaction of particles colliding with the bed, and the energy of the rebounding particle and additional ejected particles has been measured in two-dimensional situations. The research on avalanches has focused on dense, frictional flows. Experiment and numerical simulations indicate that relatively thin dense flows, on the order of ten particle diameters, occur in layers. In these, momentum transfer occurs by rubbing between contacting particles and bumping between particles falling under gravity, rather than in collisions between freely flying particles. Thicker dense flows, on the other hand, do seem to involve collisional transfer of momentum. Theories based on the appropriated mechanisms of momentum transfer predict velocity profiles that are in agreement with those measured in experiment and numerical simulations, some of which have been carried out in the course of the research.