In the last decade there has been a growing interest in the ergodic properties of infinite dimensional systems governed by stochastic partial differential equations (SPDEs). In particular, existence of attractors for two-dimensional (2-D) Navier-Stokes equations (NSEs)in bounded domains both driven by real and additive noise has been established, see e.g., [BrzCapFl93], [CrFl94], and [Schmalfuss92]. Recently in a joint work with Y. Li we have generalized the results from [CrFl94] and [Schmalfuss92] to the case of unbounded domains. We observed there that the method of asymptotical compactness used by us should work also for equations in bounded domains with much rougher noise than the original methods could handle. The main motivation of this chapter is to show that this is indeed the case for the one dimensional (1D) stochastic Burgers’ equations with additive space-time white noise. Even for readers mainly interested in the Navier-Stokes equations it could be useful to study the Burgers’ equations case. Contrary to some recent works on stochastic Burgers’ equations, see [DaPrZab6] and references therein, our approach is very similar to the approach we use for the NSEs in [BrzLi02]. The second motivation is to show that it also works for certain special form of two-dimensional (2D) stochastic NSEs with multiplicative noise. In fact, using a generalization of a recent result [CapCutl99] to bounded and unbounded domains, we show the existence of a compact invariant set for such problems. Full proofs of the results presented in this section will be published elsewhere. We should make it clear that we only study functional version of stochastic NSEs. For questions related to the pressure we refer the reader to [LRS04].