  We discuss the theoretical interpretation of observational data concerning
the clustering of galaxies at high redshifts. Building on the theoretical
machinery developed by Matarrese et al. (1997), we make detailed quantitative
predictions of galaxy clustering statistics for a variety of cosmological
models, taking into account differences in spatial geometry and initial
fluctuation spectra and exploring the role of bias as a complicating factor in
these calculations. We demonstrate that the usual description of evolution (in
terms of the parameters $\epsilon$ and $r_0$) is not useful for realistic
galaxy clustering models. We compare the detailed predictions of the variation
of correlation functions with redshift against current observational data to
constrain available models of structure formation. Theories that fit the
present-day abundance of rich clusters are generally compatible with the
observed redshift evolution of galaxy clustering if galaxies are no more than
slightly biased at $z\sim 1$. We also discuss the interpretation of a
concentration of Lyman-break galaxies found by Steidel et al. (1998), coming to
the conclusion that such concentrations are not unexpected in `standard' models
of structure formation.
