We explore the different meanings of quantum uncertainty contained in Heisenbergs seminal paper from 1927, and also some of the precise definitions that were explored later. We recount the controversy about Anschaulichkeit, visualizability of the theory, which Heisenberg claims to resolve. Moreover, we consider Heisenbergs programme of operational analysis of concepts, in which he sees himself as following Einstein. Heisenbergs work is marked by the tensions between semiclassical arguments and the emerging modern quantum theory, between intuition and rigour, and between shaky arguments and overarching claims. Nevertheless, the main message can be taken into the new quantum theory, and can be brought into the form of general theorems. They come in two kinds, not distinguished by Heisenberg. These are, on one hand, constraints on preparations, like the usual textbook uncertainty relation, and, on the other, constraints on joint measurability, including trade-offs between accuracy and disturbance.
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