The shape of flowing water When we observe fluid flows in nature, it is often because we notice the deformation of the fluid surface e.g., when light reflects on a water drop or an ocean wave. Such deformations can have great beauty and complexity, since the shape of the free surface is intimately and very nonlinearly coupled to the internal flow. In the talk, I will show examples of “simple” flows that, via a combination of inertia, gravity, friction, centrifugal forces and surface tension, generate surfaces with strong deformations, and that lead to interesting symmetry breaking transitions, where sharp corners and polygonal structures appear - even in strongly turbulent flows. The two basic examples are hydraulic jumps and rotating polygons illustrating these phenomena for laminar and turbulent flows, respectively, and it will be shown that, despite their large differences in Reynolds numbers and instability mechanism, they both rely on a transition between supercritical and subcritical flow. The phenomenon of “flow separation” will be shown to play a decisive role in the determination of flow structure and surface shape, and its importance will be further illustrated by examples from the formation and metamorphoses of sand-ripples. If time permits, I shall briefly discuss the recent attempt by Y. Couder and his collaborators to explain the mysteries of quantum mechanics by bouncing droplets moving and interacting through surface waves.