In recent years it has become clear that particular geometric structures, called positive geometries, underlie various observables in quantum field theories. In this talk I will review this connection for scattering amplitudes. After a broad review of the main ingredients involved, I will focus on maximally supersymmetric Yang-Mills theory and discuss a positive geometry encoding scattering processes in this theory -- the momentum amplituhedron. In particular, I will show how such geometry encodes the properties of amplitudes. Finally, I will discuss some of the questions which remain open in this framework.

Scattering amplitudes in N=4 super Yang-Mills theory have been extensively studied in recent years, due to their remarkable features. In particular, planar amplitudes exhibit a hidden symmetry, the dual superconformal symmetry. I will review how, together with the standard superconformal one, it forms a Yangian structure. Then I will discuss some recent results about the Yangian symmetry of light-like Wilson loops at one loop.