Abstract: 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 exciting connection for scattering amplitudes. After a broad introduction and review of the main ingredients involved, I will focus on maximally supersymmetric Yang-Mills theory and discuss a positive geometry encoding tree-level scattering processes in this theory -- the momentum amplituhedron. In particular, I will show how such geometry encodes the properties of amplitudes. Finally, I will present some of the main goals and research directions for the future.