  We study multi-dimensional normal approximations on the Poisson space by
means of Malliavin calculus, Stein's method and probabilistic interpolations.
Our results yield new multi-dimensional central limit theorems for multiple
integrals with respect to Poisson measures -- thus significantly extending
previous works by Peccati, Sol\'e, Taqqu and Utzet. Several explicit examples
(including in particular vectors of linear and non-linear functionals of
Ornstein-Uhlenbeck L\'evy processes) are discussed in detail.
