  We study galaxy clustering using halo models, where gravitational clustering
is described in terms of dark matter halos. At small scales, clustering
statistics are dominated by halo density profiles, whereas at large scales,
correlations are the result of combining non-linear perturbation theory with
halo biasing. Galaxies are assumed to follow the dark matter profiles, and
galaxy formation efficiency is given by the number of galaxies as a function of
halo mass. This approach leads to generic predictions: the galaxy power
spectrum shows a power-law behavior even though the dark matter does not, and
the galaxy higher-order correlations show smaller amplitudes at small scales
than their dark matter counterparts, as observed in galaxy catalogs. We find
that requiring to fit both the second and third order moments of the APM
galaxies provides a strong constraint on galaxy formation models. The data at
large scales require that galaxy formation be relatively efficient at small
masses, m =10^10 Msun/h, whereas data at smaller scales require that the number
of galaxies in a halo scale as the mass to the 0.8th power in the high-mass
limit. These constraints are independent of those derived from the luminosity
function or Tully-Fisher relation. We also predict the power spectrum,
bispectrum, and higher-order moments of the mass density field. Although halo
models agree well with measurements of the mass power spectrum and the higher
order Sp parameters in N-body simulations, the model assumption that halos are
spherical leads to disagreement in the configuration dependence of the
bispectrum at small scales. We stress the importance of finite volume effects
in higher-order statistics and show how they can be estimated in this approach.
