A fusion reactor must be fueled by solid pellet injection at the high field side to ensure uniform fuelling and meet the fuel cycle requirements. A reliable extrusion system must be developed to solidify and extrude the fuel in the form of a fine filament. Over the past few decades, various extrusion systems such as in-situ, piston-cylinder, single screw, twin screw extrusion were developed to progress into achieving the extrusion rate specified by ITER (International Thermonuclear Experimental Reactor). Among these techniques, twin screw extruder promises to be reliable due to its continuous operation and stable throughput. This review article has twin objectives. First, it seeks to provide an overview of developments carried out so far for the cryogenic extruders like conceptualization, prototype development and performance. The numerical modelling of cryogenic extruders is at infant stage. Therefore, the second objective of this paper is to review various numerical models from polymer extrusion research and explain the need to adopt those models to arrive at the more optimal design of an extruder. In addition, the thermo-physical properties of hydrogenic fuels are reviewed, which is very important for developing numerical models. Also, this paper brings out the critical gaps that exist in the CFD modelling of a twin screw extruder. The present review work would be of great importance to the scientific community working toward plasma fueling. © 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.