I will discuss recent work with Jonathan Block in which we develop a homotopy-theoretic version of the smooth Riemann-Hilbert correspondence. This is realized as a dg-quasi-equivalence between two dg-categories associated to a smooth compact manifold. The first can be understood as the category of representations of the infinity groupoid of the manifold. The other is the category of graded vector bundles with flat Z-graded connections on the manifold. In this way we produce a correspondence which involves the entire homotopy type of the manifold and is thus untruncated. It also involves an explicit description of the classifying space of such bundles allowing us to package the R-H correspondence as a representability statement.