Extrusion processes are widely used in industries that aim to produce advanced solutions for increasingly sophisticated demands in the plastic, food, and pharmaceutical sectors. Though the process has been in use since the 1930s, limited information is available on the analytical computation of extrusion. Generally, production has been carried out based on empirical experience and trial-and-error approaches. The development of industrial operations is, however, best addressed by modelling the processes involved, and the flow of polymer melts and fibers in extruders has been subjected to some previous studies. Also included an overview of design of a die as well as challenges in sheet/film production. This article systematically and critically reviews the literature related to the process design, machine design, process parameters, flow models, and flow analysis of extrusion with a focus on modelling the extrusion of composite materials.