  The COBE microwave background temperature fluctuations and the abundance of
local rich clusters of galaxies provide the two most powerful constraints on
cosmological models. When all variants of the standard cold dark matter (CDM)
model are subject to the combined constraint, the power spectrum of any model
is fixed to $\sim 10%$ accuracy in both the shape and overall amplitude. These
constrained models are not expected to differ dramatically in their local
large-scale structure properties. However, their evolutionary histories differ,
resulting in dramatic differences towards high redshift. We examine in detail
six standardized, COBE and cluster normalized CDM models with respect to a
large set of independent observations. The observations include correlation
function of rich clusters of galaxies, galaxy power spectrum, evolution of rich
cluster abundance, gravitational lensing by moderate -to-high redshift
clusters, $\lya$ forest, damped $\lya$ systems, high redshift galaxies,
reionization of the universe and future CMB experiments. It seems that each of
the independent observations examined is or potentially is capable of
distinguishing between at least some of the models. The combined power of
several or all of these observations is tremendous. Thus, we appear to be on
the verge of being able to make dramatic tests of all models in the near future
using a rapidly growing set of observations, mostly at moderate to high
redshift. Consistency or inconsistency between different observed phenomena on
different scales and/or at different epochs with respect to the models will
have profound implications for theory of growth of cosmic structure.
