Despite the widespread use of screw feeders in industry for transporting, metering, and processing powders, scientific understanding of their functioning is far from satisfactory. This is primarily due to the complexity of the mechanical response of powders and the complex geometry of screw feeders. In this project we have developed two models for the kinematics and mechanics of non-cohesive powders. The first model relies on several simplifying approximations, but makes the interesting prediction that the feed rate is maximum for a specific value pitch to diameter ratio of the screw. The second is a more detailed continuum model that predicts the variations of velocity, packing fraction and stress within the feeder. To validate the model predictions, we have conducted DEM simulations and gathered experimental data using a custom-built screw feeder apparatus. Overall, we find good agreement between the experimental data, DEM simulations, and model predictions for non-cohesive powders (such as glass beads). In particular, the simulations and experiments verify the model predictions of the feed rate being maximum at a certain ratio of pitch to diameter of the screw. The experiments and simulations also throw light on the variability of the feed rate, an aspect that is of concern to industry. We have conducted some experiments and DEM simulations for cohesive powders commonly used in the pharmaceutical industry. We find that the main source of variability in the feed rate is not within the feeder but at the inlet to the feeder. More detailed investigation of cohesive powders, including extension of the model to account for cohesion, remains to be done, and are the primary goals of our endeavours in the next 3 years of the project.