A comprehensive presentation of new developments in the theory of diff
use (off-specular) surface scattering of X-rays is given and illustrat
ed with experimental results on different kinds of films and surfaces.
This technique allows the determination of surface and interface morp
hology through height-height correlation spectra over a wide in-plane
wave-vector range (10(5)-10(10) m(-1)). A general method for the deter
mination of the tensorial Green function relevant to the problem is in
dicated. The Born approximation and the more accurate distorted-wave B
orn approximation are evaluated. The need for even better approximatio
ns is stated and possible methods are indicated. The theoretical resul
ts are compared with the results of experiments and non-trivial effect
s are evidenced. Finally, different methods for the measurements of li
quid fluctuation spectra with synchrotron radiation are discussed, dem
onstrating the ability of this technique to provide more insight into
the statistical physics of liquid interfaces down to molecular scales.