I review a number of tests of theories for structure formation .
Large-scale flows and IRAS galaxies indicate a high density parameter \Omega \simeq 1 , in accord with inflationary predictions , but it is not clear how this meshes with the uniformly low values obtained from virial analysis on scales \sim 1Mpc .
Gravitational distortion of faint galaxies behind clusters allows one to construct maps of the mass surface density , and this should shed some light on the large vs small-scale \Omega discrepancy .
Power spectrum analysis reveals too red a spectrum ( compared to standard CDM ) on scales \lambda \sim 10 - 100 h ^ { -1 } Mpc , but the gaussian fluctuation hypothesis appears to be in good shape .
These results suggest that the problem for CDM lies not in the very early universe — the inflationary predictions of \Omega = 1 and gaussianity both seem to be OK ; furthermore , the COBE result severely restricts modifications such as tilting the primordial spectrum — but in the assumed matter content .
The power spectrum problem can be solved by invoking a cocktail of mixed dark matter .
However , if gravitational lensing fails to reveal extended dark mass around clusters then we may be forced to explore more radical possibilities for the dark matter .