Gauge theories defined on manifolds with boundaries, be they asymptotic or at finite distance, exhibit emergent boundary degrees of freedom, sometimes referred to as edge modes. Recently, two important developments have been the realization that edge modes do even appear and play a role on fictitious entangling interfaces, and are related to the intricate asymptotic and infrared properties of theories with massless excitations, where they appear via so-called large gauge transformations and soft modes. In this talk I will review some of these results, and explain how they can be understood by a suitable generalization of the covariant phase space formalism.