I will report on a recent joint work with Nathan Perlmutter. We study the moduli space of handlebodies, i.e. the classifying space $\BDiff((D^{n+1}\times S^n)^{\natural g}, D^{2n})$ of the group of diffeomorphisms that restrict to the identity near an embedded disk $D^{2n} \subset \partial (D^{n+1}\times S^n)^{\natural g}$. We prove that there is a natural map $$ \colim_{g\to\infty}\BDiff((D^{n+1}\times S^n)^{\natural g}, D^{2n}) \; \longrightarrow \; Q_{0}BO_{2n+1}\langle n \rangle_{+} $$ which induces an isomorphism in integral homology when $n\geq 4$. Above, $BO_{2n+1}\langle n \rangle$ denotes the $n$-connective cover of $BO_{2n+1}$.