Magnesium (Mg) alloys have received a significant interest in the past 20 years, owing to a nonlinearly increasing demand for lightweight structural materials. Magnesium extrusions alloys to date have had lower industrial uptake than their counterpart aluminium extrusion alloys, predominantly due to lower extrudability and formability, tension-compression yield asymmetry and no clear advantage in the specific strength. Any improvement in extrusion alloy properties requires a better understanding of the effects of alloy composition and processing conditions; and how these dictate the final alloy microstructure. This review sheds insightful information on the processing–microstructure–property relationships of extruded magnesium alloys. Historical and recent progress in magnesium extrusion alloys is critically reviewed, including the advances in extrudability, mechanical properties and microstructural characterisation. The challenges associated with the ‘gap’ in properties between the magnesium and aluminium extrusion alloys are identified, and prospects discussed regarding the development of high performance magnesium extrusion alloys.