In their study of certain two-dimensional physical theories, Cecotti and Vafa discovered the tt*-equations. These are equations in terms of bundle data over the moduli spaces of these theories and their solutions are referred to as tt*-geometry. In this talk, based on joint work with Murad Alim and Laura Fredrickson, we study a particular class of tt*-geometry and match the tt*-equations with Hitchin’s equations. At the boundary of the corresponding moduli spaces of theories, parabolic structures naturally appear and we determine them explicitly in a wide range of examples. Finally, we comment on an oper limit of Hitchin’s equations in the parabolic framework.