  Local, or short-range, order in disordered alloys is an important and
exciting phenomenon which is quantified in electron, X-ray and neutron
scattering experiments. It is discussed in many excellent reviews and books, as
well as in the multitude of original research papers.
  This relatively short review of the subject does not attempt to discuss all
aspects of the problem of local correlations in alloys. In particular, we will
not touch such issues as multiatom (cluster) interactions, static displacements
and vibrations of alloy atoms, partially ordered, multicomponent or amorphous
alloys. As a result, we will concentrate on the Hamiltonian traditional for the
considered problem, that of the Ising model on a rigid ideal lattice with pair,
but otherwise arbitrary (i.e., of any range) interatomic interactions.
  The central object of the paper is the pair correlation function of the
corresponding dynamical variables of the model, the occupation numbers or spin
variables, the Fourier transform of which is proportional to the intensity of
diffuse scattering caused by atomic short-range order. The main aim is to show
that the expression for this quantity has certain internal structure analogous,
e.g., to that of the averaged Green's function used in the electronic theory of
disordered alloys. This structure is independent of the approximation used for
the quantitative description of correlations. As will be seen, this structure
alone, without further specification of a particular theory of short-range
order, allows us to see new possibilities in diffuse scattering, some of which
have recently been observed experimentally.
