Aluminium–air cells are high-energy density (<400 W h kg−1) primary batteries developed in the 1960s. This review shows the influence of the materials, including: aluminium alloy, oxygen reduction catalyst and electrolyte type, in the battery performance. Two issues are considered: (a) the parasitic corrosion of aluminium at open-circuit potential and under discharge, due to the reduction of water on the anode and (b) the formation of a passive hydroxide layer on aluminium, which inhibits dissolution and shifts its potential to positive values. To overcome these two issues, super-pure (99.999 wt%) aluminium alloyed with traces of Mg, Sn, In and Ga are used to inhibit corrosion or to break down the passive hydroxide layer. Since high-purity aluminium alloys are expensive, an alternative approach is to add inhibitors or additives directly into the electrolyte. The effectiveness of binary and ternary alloys and the addition of different electrolyte additives are evaluated. Novel methods to overcome the self-corrosion problem include using anionic membranes and gel electrolytes or alternative solvents, such as alcohols or ionic liquids, to replace aqueous solutions. The air cathode is also considered and future opportunities and directions for the development of aluminium–air cells are highlighted.