This chapter has discussed the gravitational instability paradigm for the formation of structure in the Universe. The detection of the Sachs-Wolfe effect by COBE, at close to the a priori predicted level provides the strongest observational support for this paradigm. The observed cellular distribution of galaxies, however, argues for some kind of hydrodynamic augmentation of the gravitational instability process. This augmentation may be the result of energy feedback from the process of galaxy formation itself. Unfortunately, this process remains unobserved.
At present, the main challenge in structure formation scenarios is to simultaneously match the large scale power with the observed clustering on small scales. Formulations of the galaxy power spectrum show that power does exist on very large scales and this simply can't be reproduced by standard CDM. Hence, somewhat exotic augmentations of CDM that act to suppress the formation of small scale structure must be present. Current data can not distinguish between these various augmentations but most all can be ruled out if H0 is greater than 70. New classes of non-zero models, however, can successfully reproduce many of the features of the power spectrum. Currently, there are no strong observational constraints against non-zero values for .