  We describe cosmological simulation techniques and their application to
studies of cosmic structure formation, with particular attention to recent
hydrodynamic simulations of structure in the high redshift universe.
Collisionless N-body simulations with Gaussian initial conditions produce a
pattern of sheets, filaments, tunnels, and voids that resembles the observed
large scale galaxy distribution. Simulations that incorporate gas dynamics and
dissipation form dense clumps of cold gas with sizes and masses similar to the
luminous parts of galaxies. Models based on inflation and cold dark matter
predict a healthy population of high redshift galaxies, including systems with
star formation rates of 20 M_{\sun}/year at z=6. At z~3, most of the baryons in
these models reside in the low density intergalactic medium, which produces
fluctuating Lyman-alpha absorption in the spectra of background quasars. The
physical description of this ``Lyman-alpha forest'' is particularly simple if
the absorption spectrum is viewed as a 1-dimensional map of a continuous medium
instead of a collection of lines. The combination of superb observational data
and robust numerical predictions makes the Lyman-alpha forest a promising tool
for testing cosmological models.
