Both the Higgs bundle moduli space and the moduli space of flat connections have a natural stratification induced by a C* action. In both of these stratifications, each strata is a holomorphic fibration over a connected component of complex variations of Hodge structure. While the nonabelian Hodge correspondence provides a homeomorphism between Higgs bundles and flat connections, this homeomorphism does not preserve the respective strata. The closed strata on the Higgs bundle side is the image of the Hitchin section (the Hitchin component) and the closed strata in the space of flat connections is the space of opers. In this talk we will show how many of the relationships between opers and the Hitchin component extend to general strata. This is based on joint work with Richard Wentworth.