simply put, a stein manifold is a closed complex submanifold of complex euclidean space. stein manifolds have rich function theory and many of their global properties can be understood with the help of sheaf cohomology. as a long term goal we would like to prove vanishing theorems for closed submanifolds of hilbert spaces, and give a cohomological characterization of these submanifolds. in this talk we survey the available results in this direction and look at the possible near future.