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A well-known theorem of Max Noether asserts that the gonality of a smooth curve $C\subset {\mathbb{P}}^2$ of degree $d\ge 4$ is $d-1$, and any morphism $C\to {\mathbb{P}}^1$ of minimal degree is obtained as the projection from one point of the curve. The most natural extension of gonality to n-dimensional varieties $X$ is the degree of irrationality, that is the minimum degree of a dominant rational map $X--\to {\mathbb{P}}^n$. This paper reports on the joint work [4] with Renza Cortini and Pietro De Poi, which aims at extending Noether's Theorem to smooth hypersurfaces $X\subset {\mathbb{P}}^{n+1}$...