  Through Cayley and Langlands type correspondences, we give a geometric
description of the moduli spaces of real orthogonal and symplectic Higgs
bundles of any signature in the regular fibres of the Hitchin fibration. As
applications of our methods, we complete the concrete abelianization of real
slices corresponding to all quasi-split real forms, and describe how extra
components emerge naturally from the spectral data point of view.
