Standards complement regulation as frameworks for Artificial Intelligence governance. Within the European Union, this complementarity is laid down as the New Legislative Framework. Standards can be harmonised to provide a presumption of conformity with regulation. They draw legitimacy from the inclusion of all relevant stakeholders as well as the consensus principle although there are limitations in practice. At both European and international levels, standardisation for generative AI is still in its infancy due to standardisation following relying on a level of technical maturity. Therefore, most activity is currently seen in the policy domain. Potential directions for future generative AI standards are suggested. Generative AI drives the need for non-AI standards, too, especially in areas of digital trust and digital identity.