The extruder is the most important processing machine in the polymer industry. Based on the economic framework, the primary objective of machine manufacturers is to increase the output rate while guaranteeing excellent melt quality. To meet the ever-increasing demands on the machinery, the process requires further optimization and thus a deeper understanding of the transport mechanisms governing physical operation. This thesis investigates the following processing steps both theoretically and experimentally: (i) melt conveying and pressurization, (ii) devolatilization, and (iii) mixing. In the first part of the thesis a new heuristic method for modeling the flow of shear-thinning polymer melts in three-dimensional metering channels is developed and validated against experimental extrusion data. The novelty of the approach lies in the construction of an analytical melt-conveying model from a large number of numerical solutions of scaled flow equations. Applying the theory of similarity, the governing flow equations are rewritten in dimensionless form and the characteristic dimensionless parameters of the system are determined. These quantities are varied to create a large set of physically independent design points, whose volume flow rates are evaluated numerically. The numerical results of the parametric design study are then approximated heuristically using symbolic regression based on genetic programming, which yields a novel melt-conveying model for single-screw extruders. The coupling between the shear-thinning flow behavior of the polymer melt and the three-dimensional velocity field in the screw channel being considered, the novel melt-flow theory enables an accurate prediction of the pumping capability of both pressure-generating and overridden melt-conveying sections. The high accuracy of the new modeling approach is numerically and experimentally confirmed. ^The second part of this thesis investigates devolatilization in vented single-screw extruders by means of a semi-numerical modeling approach. The objective is to analyze the influence of the circulatory transverse flow in the partially-filled screw channel on the mass transport of volatiles in the polymeric phase. Previous theories that modeled devolatilization in vented extruders described the transport of volatiles in molten polymers as a diffusion-controlled process, omitting the effect of surface renewal on devolatilization efficiency. This thesis derives analytical solutions for the two-dimensional circulatory flow in a partially-filled screw channel. The resulting velocity field is then related to a convection-diffusion differential equation for species transport, which is solved numerically using the finite-volume method. The results provide both qualitative and quantitative insights into how volatile depletion is related to the flow field developed. Even for low screw speeds, continuous surface renewal improves the devolatilization efficiency significantly. The third part of this thesis applies three-dimensional flow simulations to investigate mixing in block-head mixers, which are primarily distributive mixers that work by multiple disrupting the flow. The polymer-processing industry employs a variety of block-head mixers with little consensus on the design of the mixing elements. This thesis presents a numerical design study analyzing the influence of three geometrical parameters on the pumping and mixing capability of the mixing screws: (i) number of flights, (ii) number of blocks, and (iii) stagger angle between the blocks. The results increase the understanding of mixing in block-head mixers and present design guidelines to optimize both the pressure consumption and viscous heating in the screw channel as well as distributive and dispersive mixing.