  Theoretical models for structure formation with Gaussian initial fluctuations
have been worked out in considerable detail and compared with observations on
various scales. It is on nonlinear scales $\lsim 10 \ h^{-1}\ {\rm Mpc}$ that
the greatest differences exist between $\Omega=1$ models that have been
normalized to agree on the largest scales with the COBE data; here especially
there is a need for better statistical tests which are simultaneously {\it
robust}, {\it discriminatory}, and {\it interpretable}. The era at which galaxy
and cluster formation occurs is also a critical test of some models. Needs for
the future include faster and cleverer codes, better control of cosmic variance
in simulations, better understanding of processes leading to galaxy formation,
better ways of comparing observational data with models, and better access to
observational and simulation data.
