Human oversight has been much stressed and discussed as a safeguarding measure to ensure human centrism in AI deployment. Through its proposal of a new EU Artificial Intelligence Act, the Commission is breaking new ground by promoting the introduction of the first general and sharp worded human oversight requirement over AI systems in European law. This Article discusses the content, limitations and implications of this oversight requirement. It does this by addressing the questions of what the Regulation prescribes on 'what' is to be overviewed, 'when' the overview is to be exercised and 'by whom'. The article points to some of the AIA's unclarities and gaps, and to the implications of vesting too much trust in providers to secure the oversight infrastructure of high-risk AI systems.