In this chapter, we attempt to clarify the EU governance framework for Artificial Intelligence (AI) by describing its—still brief—history. We do this under the guidance of the question: what has and might in the future become of the typical approach in terms of ethics rather than of new legislation that characterised EU AI governance in its earliest stages? We do so not only because we believe this clarification will enable a better understanding of the developments in the EU governance of AI during the past years and the years to come, but also because this ethics approach might harbour a surplus value that cannot be completely or efficiently replaced by new legislation alone. For this reason, we will go to some lengths to explain the relevant differences between the ethics-approach on the one hand, and new legislation as an alternative to it, on the other, and to reflect critically on them. In this manner, we hope to deliver relevant considerations for an evaluation of the adequacy of the AI Act and the EU’s governance of AI in general.