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Over the last twenty years there has been a growing evidence that the standard formulation of Quantum field theory using path integrals and Feynman diagrams fails to explain unexpected simplicity and hidden symmetries of the scattering amplitudes. I show that in the case of planar maximally supersymmetric Yang-Mills theory there exists a radically different picture for amplitudes as volumes of the "Amplituhedron" which is a higher-dimensional generalization of convex polygons to Grassmannians. In this approach, the central physical principles of locality and unitarity become derived concepts from the Amplituhedron geometry, while the usually hidden symmetries become manifest.