Quantum and statistical theories provide a consistent framework for a physical description at the atomic scale. At the other extreme, the study of macroscopic physics is provided by the continuum theory where all internal structure of the medium is implicity averaged out. However, there exist numerous physical situations lying at intermediate scales where neither statistical nor continuous available theories are satisfactory. Starting from continuum physics but using weaker assumptions, different attempts have been performed, in order to introduce interfacial mechanical, thermodynamical and electromagnetic contributions adding thus interfacial differential equations to the well-known jump relations. Although the idea is conceptually simple and physically more realistic than the classical formulations, one runs into serious mathematical difficulties. These aspects are discussed, then an energy approach that applies to both mechanics and electromagnetism is proposed. The latter generalizes the well-known Lagrangian approach so that non integrable physical situations may be included (irreversible processes). This new theory is based on three invariance principles: scale-change, gauge and rotational invariances. The first of these is of a mathematical nature, it allows a passage from continuous to discontinuous media evading thus the difficulty associated with distribution multiplications. The other two principles are of a physical nature and they govern the electromagnetic and the mechanical fields. Comparisons are performed with previous works and physical examples are given where the classical methods do not apply.