The boundary problem is the failure to associate a symplectic structure to a gauge theory over a bounded region of spacetime. Two strategies to circumvent this problem have been much discussed in the recent literature: the edge mode approach by Donnelly & Freidel, and the connection approach by Gomes & Riello. Relying on the bundle geometry of field space, we attempt to make them more systematic, so as to facilitate comparison and to shed some light on conceptual aspects. We illustrate the general results with the standard examples of Yang-Mills theory, the Cartan formulation of General Relativity, and Chern-Simons theory -- thereby reproducing several results of the literature.