  This paper reviews the measurements of galaxy correlations at high redshifts,
and discusses how these may be understood in models of hierarchical
gravitational collapse. The clustering of galaxies at redshift one is much
weaker than at present, and this is consistent with the rate of growth of
structure expected in an open universe. If $\Omega=1$, this observation would
imply that bias increases at high redshift, in conflict with observed $M/L$
values for known high-$z$ clusters. At redshift 3, the population of
Lyman-limit galaxies displays clustering which is of similar amplitude to that
seen today. This is most naturally understood if the Lyman-limit population is
a set of rare recently-formed objects. Knowing both the clustering and the
abundance of these objects, it is possible to deduce empirically the
fluctuation spectrum required on scales which cannot be measured today owing to
gravitational nonlinearities. Of existing physical models for the fluctuation
spectrum, the results are most closely matched by a low-density spatially flat
universe. This conclusion is reinforced by an empirical analysis of CMB
anisotropies, in which the present-day fluctuation spectrum is forced to have
the observed form. Open models are strongly disfavoured, leaving $\Lambda$CDM
as the most successful simple model for structure formation.
