Higgs bundles are holomorphic objects which have become useful for understanding representations of the fundamental group of a closed surface into a Lie group. In this talk, we will present an overview of their theory, and how the Non-abelian Hodge correspondence can be used to study individual representations and their moduli spaces.

We will also present a variation of the correspondence known as the conformal limit, which, together with the correspondence, allows one to build complex projective structures naturally associated with these representations. This is joint work with Peter B. Gothen.