Given a fixed convex body $K$, choose $n$ points randomly on the boundary of $K$ according to a ``uniform" distribution, and call the convex hull of these $n$ points a Random Inscribing Polytope. We will discuss some recent asymptotic results on the volume of these polytopes. Namely, we will prove a lower bound on the variance, some concentration result, and an analogue of the central limit theorem. This is joint work with Ross Richardson and Van Vu.