Stochastic analysis on the fluid dynamics PDE, mainly the Navier-Stokes equations forced by random noise, goes back for decades, e.g. the work of Bensoussan and Temam in 1973. The study of well-posedness and ergodicity in particular have caught much attention from many mathematicians. In this talk I will discuss some developments in these directions of research, in particular the difficulty that arises in comparison to the deterministic case (no random noise) and upon generalizing to other systems of fluid PDEs that are more complex than the Navier-Stokes equations.