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A K”unneth structure on a smooth manifold is given by a symplectic form together with two complementary Lagrangian foliations. These structures arise naturally in geometry, in dynamical systems, and in high-energy physics.They have been studied from many different points of view, including, among others, those of symplectic geometry,  of pseudo-Riemannian geometry, and of para-complex geometry. I will discuss some  motivating examples, explain the basic features of K”unneth structures, and exhibit non-trivial examples, without assuming any background beyond elementary differential geometry.