Supersymmetric theories with 8 supercharges in dimensions 3 through 6 have a large moduli space of vacua, and the Higgs branches are one of the most significant parts of this space. These (singular) hyper-Kahler spaces can be characterised by a combinatorial object known as the magnetic quiver. By using this technique, we can fully encode the Higgs branch geometry for both the low energy effective description and the strongly coupled conformal fixed point. A simple algorithm on the magnetic quiver allows us to access the stratification of the Higgs branch, which physically corresponds to the generalised Higgs mechanism. In this talk, I will discuss this construction in the context of 5d and 6d theories.