The cosmic background radiation is thermal radiation with a temperature of 2.75 K still present throughout the universe, a relic of its hot, big bang, initial phase. Detailed studies of this radiation, and particularly its angular variations, can provide information obtainable in no other way about the global geometry and expansion of the universe, about the distribution of mass near our Galaxy, and about the process of galaxy formation. This review treats searches for such angular variations and the consequences of the resulting measurements of, or upper limits on, variations in the cosmic background radiation.The only unambiguously detected angular variation is the dipole component of the radiation, believed to arise from a Doppler shift due to the motion of the Earth; the inferred velocity of the Earth relative to the background is -350 km s-'. Searches for a quadrupole component have found none, with upper limits on the fractional variation, A T / T , of a few times IO-'. The absence of a significant quadrupole moment allows us to reject many models for the universe which include anisotropic expansion or shear. These constraints are reinforced by upper limits on the linear polarisation of the cosmic background radiation.Searches for smaller scale variations, at angles from arcseconds to degrees, have thus far failed to find any. At some angular scales, upper limits on temperature fluctuations have now reached a level of a few times Reviewed here are both the observational methods employed in such searches and some of the sources of statistical and systematic errors encountered. Several consequences of the upper limits on fluctuations in the radiation are examined. Among these are constraints on models for the formation of large astronomical systems like galaxies, and the support these observations lend to models for the very early expansion of the universe which arise from new theories in particle physics.An outline of big bang cosmology is contained in an appendix for readers unfamiliar with the nomenclature of cosmology.