This review begins with the classical foundations of relative dispersion in
Kolmogorov's similarity scaling. Analysis of the special cases of isotropi
c and homogeneous scalar fields is then used to establish most simply the c
onnection with turbulent mixing. The importance of the two-particle acceler
ation covariance in relative dispersion is demonstrated from the kinematics
of the motion of particle-pairs. A summary of the development of two-parti
cle Lagrangian stochastic models is given, with emphasis on the assumptions
and constraints involved, and on predictions of the scalar variance field
for inhomogeneous sources. Two-point closures and kinematic simulation are
also reviewed in the context of their prediction of the Richardson constant
and other fundamental constants. In the absence of reliable field data, di
rect numerical simulations and laboratory measurements seem most likely to
provide suitable data with which to test the assumptions and predictions of
these theories.