INTRODUCTION For decades screw extrusion is the most important continuous process step of polymer processing. Single and multi-screw extruders are the heart of many extrusion plants. Due to the economic importance and the complex transport phenomena in plasticating extruders screw extrusion is subject of current research. This paper deals with current achievements in experimental and computational modeling of single and twin screw plasticating extrusion. COMPUTATIONAL MODELING For computational modeling following advanced methods were used: DEM (discrete element modeling) LIGGGHTS® for solid conveying, network theory for phase transition resp. melting for barrier screw types and a generalized analytic equation for the pressure-throughput behaviour, developed by using an evolutionary heuristic optimization algorithm, for melt conveying. Additionally a parameterized creation of twin screw geometry for counter as well as co-rotating extruders by using analytic equations and triangulation is used for CFD simulation in order to reduce the most time consuming step of CFD simulation (compared with the simulation and post-processing step), the pre-processing. EXPERIMENTAL MODELING Not only for validation, but also to deepen the knowledge regarding the transport phenomena in plasticating extruders and to study the performance in terms of productivity and quality computational modeling was supplemented with procedural instructions for experimental modeling including the determination of pressure-throughput behaviour, energy and thermal monitoring by using temperature gradient sensors, axial pressure profile inside the barrel, radial temperature distribution inside the melt tube after the extruder screw, residence time distribution and self-cleaning time by using fluorescence spectroscopy, mixing performance by applying grey value analysis and change of molar mass distribution.