  Let $K$ be a smooth convex set with volume one in $\BBR^d$. Choose $n$ random
points in $K$ independently according to the uniform distribution. The convex
hull of these points, denoted by $K_n$, is called a {\it random polytope}. We
prove that several key functionals of $K_n$ satisfy the central limit theorem
as $n$ tends to infinity.
