  We develop an analytic theory for the redshift space bispectrum of dark
matter, haloes and galaxies. This is done within the context of the halo model
of structure formation, as this allows for the self-consistent inclusion of
linear and non-linear redshift space distortions and also for the non-linearity
of the halo bias. The model is applicable over a wide range of scales: on the
largest scales the predictions reduce to those of the standard perturbation
theory (PT); on smaller scales they are determined primarily by the nonlinear
virial velocities of galaxies within haloes, and this gives rise to the
U-shaped anisotropy in the reduced bispectrum -- a finger print of the
Finger-Of-God distortions. We then confront the predictions with bispectrum
measurements from an ensemble of numerical simulations. On very large scales,
k=0.05 h/Mpc, we find reasonably good agreement between our Halo Model, PT and
the data, to within the errors. On smaller scales, k=0.1 h/Mpc, the measured
bispectra differ from the PT at the level of 10-20%, especially for colinear
triangle configurations. The Halo Model predictions improve over PT, but are
accurate to no better than 10%. On smaller scales k=0.5-1.0 h/Mpc, our model
provides a significant improvement over PT, which breaks down. This implies
that studies which use the lowest order PT to extract galaxy bias information
are not robust on scales k>0.1 h/Mpc. The analytic and simulation results also
indicate that there is no observable scale for which the configuration
dependence of the reduced bispectrum is constant--hierarchical models for the
higher order correlation functions in redshift space are unlikely to be useful.
It is hoped that our model will facilitate extraction of information from
large-scale structure surveys of the Universe.
