  We review the formalism and applications of the halo-based description of
nonlinear gravitational clustering. In this approach, all mass is associated
with virialized dark matter halos; models of the number and spatial
distribution of the halos, and the distribution of dark matter within each
halo, are used to provide estimates of how the statistical properties of large
scale density and velocity fields evolve as a result of nonlinear gravitational
clustering. We first describe the model, and demonstrate its accuracy by
comparing its predictions with exact results from numerical simulations of
nonlinear gravitational clustering. We then present several astrophysical
applications of the halo model: these include models of the spatial
distribution of galaxies, the nonlinear velocity, momentum and pressure fields,
descriptions of weak gravitational lensing, and estimates of secondary
contributions to temperature fluctuations in the cosmic microwave background.

Astrophysics