In this thesis quantum field theories with 8 supercharges, and especially their moduli spaces, are studied. A collection of methods are used to study these singular moduli spaces, such as counting gauge invariant operators via means of a Hilbert series, brane realisations, and computation of their singularity structure in terms of a Hasse diagram. A particular focus lies on an explanation of this Hasse diagram as a geometric realisation of the Higgs mechanism. The moduli space of quantum chromodynamics with 8 super- charges is discussed in great detail. After this more complicated theories are discussed, in particular ones, where the Higgs branch consists of multiple cones.