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In this talk I will discuss some recent results on boundary degrees of freedom (or edge modes), and their description via an extended phase space structure containing extra boundary fields. Motivated by a slight modification of the covariant phase space formalism, I will show how the use of a boundary Lagrangian enables to include the edge modes in the phase space and to obtain their boundary dynamics. This will be illustrated on the example of Maxwell theory, where in addition the edge modes can be understood as contributing to entanglement entropy. The possible extension of this result to gravity will then be mentioned.