I will discuss how much randomness one needs for the infinite dimensional diffusion associated an stochastic partial differential equation (SPDE) to be ``elliptic´´. Along the way I will consider hypoeelipticity for SPDEs. Most of the discussion will be framed in terms of the ergodic or long time behavior of the systems. I will talk about some concrete examples such and the Navier-Stokes equations and Reaction Diffusion Equations.