Most cosmologists now believe that we live in an evolving universe that has been expanding and cooling since its origin about 15 billion years ago. Strong evidence for this standard cosmological model comes from studies of the cosmic microwave background radiation (CMBR), the remnant heat from the initial fireball. The CMBR spectrum is blackbody, as predicted from the hot Big Bang model before the discovery of the remnant radiation in 1964. In 1992 the cosmic background explorer (COBE) satellite finally detected the anisotropy of the radiation-fingerprints left by tiny temperature f luctuations in the initial bang. Careful design of the COBE satellite, and a bit of luck, allowed the 30 K f luctuations in the CMBR temperature (2.73 K) to be pulled out of instrument noise and spurious foreground emissions. Further advances in detector technology and experiment design are allowing current CMBR experiments to search for predicted features in the anisotropy power spectrum at angular scales of 1°and smaller. If they exist, these features were formed at an important epoch in the evolution of the universe-the decoupling of matter and radiation at a temperature of about 4,000 K and a time about 300,000 years after the bang. CMBR anisotropy measurements probe directly some detailed physics of the early universe. Also, parameters of the cosmological model can be measured because the anisotropy power spectrum depends on constituent densities and the horizon scale at a known cosmological epoch. As sophisticated experiments on the ground and on balloons pursue these measurements, two CMBR anisotropy satellite missions are being prepared for launch early in the next century.In the standard hot Big Bang cosmological model, cosmic microwave background radiation (CMBR) is the remnant thermal radiation which dominated the development of the very early universe. Its currently observed properties give us an important means of testing the standard model and of studying physical processes in the universe beyond the reach of our most powerful optical telescopes. Measurements by the cosmic background explorer (COBE) satellite show that the CMBR spectrum between wavelengths of 5 mm and 0.5 mm is the same as that of a blackbody emitter with an accuracy of Ϯ0.01% (1), in surprisingly good agreement with predictions based on the hot Big Bang model. Of secondary interest to cosmology, the CMBR temperature is measured as 2.728 Ϯ 0.004 K. The absence of spectral distortions in the CMBR imposes limits on energy-producing processes in the universe from an age of t Ϸ 1 year to an age of t Ϸ 10 8 years. Another critical test of the standard model is to measure and characterize the CMBR anisotropies expected from density perturbations at t Ϸ 3 ϫ 10 5 years, when the matter becomes neutral and decouples from the thermal radiation for the first time. Theorists predicted CMBR anisotropies of about 1 part in 10 5 (␦T Ϸ 30 K), corresponding to the mass density perturbations needed to seed the mass structure seen in the universe today. In 1992 th...