  We present a survey on the moduli spaces of rank 2 quadric bundles over a
compact Riemann surface X. These are objects which generalise orthogonal
bundles and which naturally occur through the study of the connected components
of the moduli spaces of Higgs bundles over X for the real symplectic group
Sp(4,R), with non-maximal Toledo invariant. Hence they are also related with
the moduli space of representations of $\pi_1(X)$ in Sp(4,R). We explain this
motivation in some detail.
