  After two decades of direct dynamical simulation of large-scale structure in
the universe, it is safe to say the subject is now mature. Still, there are
parts of the problem that are less well developed than others. In general, the
collisionless dynamics of the dark matter component is better understood than
the collisional gas dynamics of the baryonic component. In situations where the
gas dynamics is relatively simple, such as the Lyman-$\alpha$ forest and the
intracluster medium in X-ray clusters, our ability to reproduce observational
data has evolved rapidly, and the interpretive and predictive power of such
experiments should now be taken seriously. A comparison of twelve gas dynamic
codes to the problem of forming a single X-ray cluster shows that numerical
inaccuracies are modest (typically below ten percent), leaving missing physics
as the main source for large systematic differences between theory and
observation. Galaxy formation, being more complex, is farther behind in its
development, but simulations capable of resolving the morphological range of
the Hubble sequence in cosmologically interesting volumes may be just around
the corner.
