After briefly reviewing some of the high-precision experimental confirmations of General Relativity (GR), the talk will discuss some open issues concerning both physical and mathematical aspects of GR, notably: . Tantalizing links between GR and Yang-Mills theory ; . Links between Einstein equations and Navier-Stokes equations; . Emergence of hidden symmetry structures near cosmological singularities; . Peeling properties and symmetry structures near infinity; . Skeletonization of Black Holes as point masses; . Scarcity of viable extensions of GR.