Abstract: In compactifications of M-Theory, ADE singularities are expected to give rise to non-abelian gauge theories. In case the compactification manifold admits an torus fibration (this case is usually called `F-theory') such singularities become degenerations of the fibre. These degenerations have a nice classification due to Kodaira for complex surfaces, but no such classification exists in higher dimensions. In this talk, I will present some recent observations on the interplay between singular fibres and the effective low-energy physics in F-theory.