Observational limits on the microwave-background-radiation anisotropy on various angular scales are reviewed. Comparison is made with the predictions of the gravitational-instability theory of galaxy formation from primordial fluctuations in the very early universe. There is no entirely satisfactory theory that presently reconciles inflationary cosmology predictions of the flatness of the universe and of the scale-invariant primordial fluctuation spectrum with the limits on the amplitude of the anisotropy (δT/T), with the Virgo-cluster motion inferred from the dipole anisotropy, and with astronomical determinations of the cosmological density parameter.