This paper argues that spacetime visualisability is not a necessary condition for the intelligibility of theories in physics. Visualisation can be an important tool for rendering a theory intelligible, but it is by no means a sine qua non. The paper examines the historical transition from classical to quantum physics, and analyses the role of visualisability and its relation to intelligibility. On the basis of this historical analysis, an alternative conception of the intelligibility of scientific theories is proposed, based on (...) Heisenberg 's reinterpretation of the notion of Anschaulichkeit. (shrink)