  We develop a new geometric method of understanding principal G-Higgs bundles
through their spectral data, for G a real form of a complex Lie group. In
particular, we consider the case of G a split real form, as well as G =
SL(2,R), U(p,p), SU(p,p), and Sp(2p,2p). Further, we give some applications of
our results, and discuss open questions.
