The optical properties of plasmonic nanostructures supporting Fano resonances are investigated with an electromagnetic theory. Contrary to the original work of Fano, this theory includes losses in the materials composing the system. As a result, a more general formula is obtained for the response of the system and general conclusions for the determination of the resonance parameters are drawn. These predictions are verified with surface integral numerical calculations in a broad variety of plasmonic nanostructures including dolmens, oligomers, and gratings. This work presents a robust and consistent analysis of plasmonic Fano resonances and enables the control of their line shape based on Maxwell's equations. The insights into the physical understanding of Fano resonances gained this way will be of great interest for the design of plasmonic systems with specific spectral responses for applications such as sensing and optical metamaterials.