An ab initio theory for Fano resonances in plasmonic nanostructures and metamaterials is de- veloped using Feshbach formalism. It reveals the role played by the electromagnetic modes and material losses in the system, and enables the engineering of Fano resonances in arbitrary geome- tries. A general formula for the asymmetric resonance in a non-conservative system is derived. The influence of the electromagnetic interactions on the resonance line shape is discussed and it is shown that intrinsic losses drive the resonance contrast, while its width is mostly determined by the coupling strength between the non-radiative mode and the continuum. The analytical model is in perfect agreement with numerical simulations.