Since the mid-1970s there have been many reports that purport to implicate aluminium in the etiology of neurodegenerative disease. After several decades of research, the role of aluminium in such disease remains controversial and is not the subject of this review. However, if aluminium is implicated in such disease then it follows that there must be a toxicological mechanism, or mode of action, and many researchers have investigated various potential mechanisms including the involvement of oxidative damage, cytotoxicity, and genotoxicity. This paper reviews many of the publications of studies using various salts of aluminium and various genotoxicity endpoints, both in vitro and in vivo, with a focus on oxidative damage. The conclusion of this review is that the majority, if not all, of the publications that report positive results have serious technical flaws and/or implausible findings, and consequently should contribute little or no weight to a weight of evidence (WoE) argument. There are many high quality, GLP compliant genotoxicity studies, that follow relevant OECD test guidelines and the ECHA integrated mutagenicity testing strategy, on several salts of aluminium; all demonstrate clear negative results for both in vitro and in vivo genotoxicity. In addition, the claim for an oxidative mode of action for aluminium can be shown to be spurious. This review concludes that there are no reliable studies that demonstrate a potential for genotoxicity, or oxidative mode of action, for aluminium.