In many ways irreducible symplectic manifolds behave similar to K3-surfaces, although it is known that the global Torelli theorem fails in general. Nevertheless, it is possible to relate moduli spaces of polarized irreducible symplectic manifolds to quotients of type IV domains by an arithmetic group. We will give an introduction to the subject and sketch a proof that certain moduli spaces of polarized irreducible symplectic manifolds are of general type.This is joint work with V. Gritsenko and G.K. Sankaran.