We propose a novel polymer extrusion process, known as the solid state shear extrusion pulverization and modification (SSSE process), based on the simultaneous action of shear deformation and pressure at selected temperatures. This process can be used for continuous pulverization and copulverization of various polymers, including different blends, filled materials, thermoplastics, vulcanized rubbers, crosslinked polymers, polymer composites, and natural polymers. Various aspects of this process are considered, including unusual microstructure and properties of powders, low energy consumption, and mechanochemical effects. Possible applications of SSSE to polymer/rubber recycling and to obtaining advanced polymer powders and modified powders are considered, together with scaling-up problems of equipment suitable for industrial application.