Current observational constraints on anisotropies in the cosmic microwave background (CMB) and on the clustering of galaxies have considerably narrowed the range of acceptable models for galaxy formation. Observations of these anisotropies on intermediate and large angular scales provide the best constraint on the amplitude of very long wavelength density fluctuations. Results from the Tenerife CMB fluctuation experiment at intermediate angular scales (6 deg) are presented which, taken together with recently reported upper limits to fluctuations on small (arcmin) angular scales, constrain severely the spectral index of initial fluctuations in baryon dominated model universes. Constraints on adiabatic fluctuations in 'hot' and 'cold' dark matter models are also briefly discussed.