Important developments in extrusion have taken place over the past decade, both in equipment and theory. Several of these will be discussed in this keynote lecture. Examples are high speed single screw extruders, extruders with grooved barrels and the discrete element method for detailed analysis of the flow of solid particulate materials. Some remaining challenges will be addressed as well. One of these is the development of theories that can reliably predict process instabilities. Another is the development of single screw extruders that can achieve dispersed solids melting. Also, improvement is needed in our understanding of die lip buildup as well as the effect of various coatings and surface treatments in polymer melt flow in extruders.