This review is intended to provide a flavor of the variety of
numerical cosmological calculations that have been performed to
investigate different phenomena throughout the history of our
Universe. The topics discussed range from the strong field
dynamical behavior of spacetime geometry at early times near the
Big Bang singularity and the epoch of inflation, to the late time
evolution of large scale matter fluctuations and the formation of
clusters of galaxies. Although many problems have been addressed,
the complexity of the varied physical processes in the extreme
time, spatial, and dynamical scales of our Universe guarantees
that many more interesting and unresolved issues remain. Indeed,
even the background cosmological model which best describes our
Universe is essentially unknown. The topology of our Universe,
the generic singularity behavior, the fundamental nonlinear field
and gravitational wave interactions, the existence and role of a
cosmological constant, the correct structure formation scenario,
and the origin and spectrum of primordial fluctuations, for
example, are uncertain. However the field of numerical cosmology
has matured, in the development of computational techniques, the
modeling of microphysics, and in taking advantage of current
computing technologies, to the point that it is now possible to
perform reliable comparisons of numerical models with observed
data.