This paper gives a personal view on the state of art in relation to the modelling of polymer melt processing. The paper briefly reviews both industrial, laboratory and modelling developments over the last forty years and highlights the key aspects now required for realistic modelling of polymer melt extrusion processing. The paper summarizes elements relating to the numerical simulation of specific and general polymer processes and also provides topical examples of the application of numerical modelling to certain commercial processes. The paper concludes with identifying areas of polymer processing that still remain a challenge in relation to accurate prediction.