This chapter analyses the public and private governance structure of the EU AI Act (AIA) and its associated ecosystem of compliance and conformity. Firstly, the interaction of public and private governance in the making of AI law meant to concretise the rules in the AIA is analysed. Secondly, the focus shifts to the interaction of public and private governance in the Act’s enforcement through compliance, conformity and public authorities. Thirdly, it is argued that the EU legislature has neither fully developed public private governance nor the interaction between the two. As a result, there are many gaps in the involvement of civil society in compliance, conformity and enforcement of private regulations, in particular harmonized technical standards, Codes of Practice and Codes of Conduct. Moreover, the extreme complexity of the AIA’s governance structure is likely to trigger litigation between AI providers and deployers and the competent surveillance authorities, or more generally in B2B and B2C relations.