  Understanding inhomogeneous and anisotropic fluid flows require mathematical
and computational tools that are tailored to such flows and distinct from
methods used to understand the canonical problem of homogeneous and isotropic
turbulence. We review some recent developments in the theory of inhomogeneous
and anisotropic turbulence, placing special emphasis on several kinds of
quasilinear approximations and their corresponding statistical formulations.
Aspects of quasilinear theory that have received insufficient attention in the
literature are discussed, and open questions are framed.
