The interactions of light with metamaterial structures can be extremely complex to investigate especially when vectorial fields, oblique propagation directions, and multipolar contributions are considered. To ease the modelling procedure of metamaterials, a convenient and powerful theoretical framework is developed by connecting the spatial symmetries of these structures to their electromagnetic and scattering properties. This greatly reduces the complexity of the problem since only the relevant symmetry-invariant material properties and scattering parameters can be unambiguously identified. This opens the door for modelling elaborate structures that would be otherwise nearly impossible to theoretically describe.