  A brief review is given of recent results devoted to the effects of
large-scale anisotropy on the inertial-range statistics of the passive scalar
quantity $\theta(t,{\bf x})$, advected by the synthetic turbulent velocity
field with the covariance $\propto\delta(t-t')|{\bf x}-{\bf x'}|^{\eps}$.
Inertial-range anomalous scaling behavior is established, and explicit
asymptotic expressions for the structure functions $ S_n (\r) \equiv <
[\theta(t,{\bf x}+\r)-\theta(t,{\bf x})]^{n}>$ are obtained; they are
represented by superpositions of power laws with universal (independent of the
anisotropy parameters) anomalous exponents, calculated to the first order in
$\eps$ in any space dimension. The exponents are associated with tensor
composite operators built of the scalar gradients, and exhibit a kind of
hierarchy related to the degree of anisotropy: the less is the rank, the less
is the dimension and, consequently, the more important is the contribution to
the inertial-range behavior. The leading terms of the even (odd) structure
functions are given by the scalar (vector) operators. The small-scale
anisotropy reveals itself in odd correlation functions: for the incompressible
velocity field, $S_{3}/S_{2}^{3/2}$ decreases going down towards to the depth
of the inertial range, while the higher-order odd ratios increase; if the
compressibility is strong enough, the skewness factor also becomes increasing.
