Atmospheric and oceanic eddies are believed to be manifestations of quasigeostrophic turbulence-turbulence that occurs in rapidly rotating, vertically stratified fluid systems. The heat, momentum, and water transport by these eddies constitute a significant component of the climate balance, without which climate change cannot be understood. A major, unsolved problem is whether the turbulent eddy fluxes can be parameterized in terms of the large-scale, background flow. In the past, stochastic models have been used quite extensively to investigate quasigeostrophic turbulence in the case in which the eddy statistics are isotropic and homogeneous. Unfortunately, these models ignore the background shear which is absolutely essential to maintaining the eddies in the presence of dissipation. Recent attempts to extend stochastic models to shear flows have shown significant skill in predicting the structure of the eddy fluxes in arbitrary, three-dimensionally varying flows. This paper provides an accessible introduction to these models. The topics reviewed include quasigeostrophic turbulence and two-dimensional turbulence, non-modal and optimal perturbations, mathematical theory of stochastic models, stochastic model simulations with realistic background states, and recent closure theories. A list of unsolved problems concludes this review.
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