The use of stochastic differential equations (SDE's) in applications is ubiquitous. Whether it is, to name just a few, physics, biology, or finance, SDE's allow one to incorporate an element of randomness into deterministic dynamical systems. Similar to the ordinary or partial differential equation setting, it is desirable to know that solutions to SDE's exist and, as time evolves, approach (in some sense) a unique statistical steady state. In this talk, I will highlight techniques used to study ergodicity of specific (possibly degenerate) SDE's that arise in turbulence theory. I will point to some results and also advertise open problems.