Approximating Euclidean convex domains by polyhedra is a classical topic in convex geometry and random analogues of such questions are well investigated in stochastic geometry. While notions of convexity have been studied in several complex variables (SCV) however study of polyhedral approximations is relatively new.  In this talk, we will present some recent progress on random polyhedral approximations in the context of several complex variables. We will discuss differences with optimal polyhedral approximation in SCV as well as contrast the SCV results with those in the Euclidean setting.  The talk will be based on a joint work with Siva Athreya and Purvi Gupta.