The paper presents a review of the literature and authors’ research on the current achievements in the field of extrusion of aluminium alloys, magnesium alloys, powders and aluminium-based composites in particular. The microstructure transformations taking place during homogenisation of billets from the medium- and high-strength heat-treatable aluminium alloys are still an object of interest of researchers. The recently published papers are related to dissolution of soluble phases formed during solidification and elimination of microsegregation, precipitation of the dispersoids, insoluble phases’ transformation as well as particles re-precipitation during cooling. The novelties in the extrusion of magnesium alloys and aluminium-based composites are shortly reported. Specifics of the extrusion dies design and their working conditions, which limit the products quality and working life of the tools, are extensively reported. The computer-aided designing (CAD) and finite-element method (FEM) and 3D optical scanning were used in analysis aimed at dimensional deviations of the dies and the extruded products. The surface engineering techniques such as welding techniques, diffusion layers and protective coatings such as produced by physical vapour deposition (PVD), plasma-enhanced physical vapour deposition (PAPVD), chemical vapour deposition (CVD) and plasma-enhanced chemical vapour deposition (PECVD) are described. Various original methods of extrusion including the severe plastic deformation processes (SPD), such as cyclic extrusion compression (CEC), equal-channel angular pressing (ECAP) and hydrostatic extrusion (HE) are discussed. The above techniques as well as the new KOBO extrusion process with oscillating die movement generate significant refining of the microstructure of metals and alloys and enable consolidation of the powdered materials. The application of the rapid solidification process connected with the hot extrusion permits production of beneficial microstructure and above-standard mechanical properties of the extruded products. Finally, the opportunities and directions of development of the extrusion process of metals and alloys are indicated.