This talk is about a simple but rich model problem at the cross section of stochastic homogenization and singular stochastic PDE: We consider a drift-diffusion process with a time-independent and divergence-free random drift that is of white-noise character. As already realized in the physics literature, the critical case of two space dimensions is most interesting: The elliptic generator requires a small-scale cut-off for well- posedness, and one expects marginally super-diffusive behavior on large scales. I will explain the criticality of the two-dimensional case in the introductory course by scaling arguments. […]