  We present a survey of the computation of the BPS spectrum of a general
four-dimensional N=2 supersymmetric gauge theory in terms of the Representation
Theory of quivers with superpotential. We focus on SYM with a general gauge
group G coupled to standard matter in arbitrary representations of G
(consistent with a non--positive beta--function). The situation is particularly
tricky and interesting when the matter consists of an odd number of
half-hypermultiplets: we describe in detail SU(6) SYM coupled to half a 20,
SO(12) SYM coupled to half a 32, and E_7 SYM coupled to half a 56.
