This timely review covers all aspects of three decades of study of this ghostly remnant of the hot Big Bang origin of the Universe, and examines the consequences for astrophysics, cosmology and theories of the evolution of large-scale cosmic structure. The observational techniques used to measure the spectrum of CBR and its angular distribution on the sky are examined in clear but critical detail: from the work of Penzias and Wilson in 1964 to the latest results from NASA's Cosmic Microwave Background Explorer (COBE) satellite. This review takes these observations and shows how they have...