We review theory and experiment for the mixing of a passive scalar by a tur
bulent flow. If the scalar fluctuations are maintained steady by a uniform
large scale gradient, the one-point distribution function of the scalar has
exponential tails; a property readily explained in terms of the Lagrangian
Green's function in path integral form. For higher order correlations and
separations within the scaling regime of the turbulence itself, new anomalo
us exponents have been derived from the Hopf equation, expressing the stati
onarity of the correlation functions. We concentrate on the 3-point correla
tor whose sealing exponent is very different from Kolmogorov or mean field
theory, and for which laboratory experiments can be compared with numerical
solutions of the Hopf equation, and analytic theory based on representatio
ns of the group SL(2).