  This review describes the discovery of the cosmic microwave background
radiation in 1965 and its impact on cosmology in the 50 years that followed.
This discovery has established the Big Bang model of the Universe and the
analysis of its fluctuations has confirmed the idea of inflation and led to the
present era of precision cosmology. I discuss the evolution of cosmological
perturbations and their imprint on the CMB as temperature fluctuations and
polarization. I also show how a phase of inflationary expansion generates
fluctuations in the spacetime curvature and primordial gravitational waves. In
addition I present findings of CMB experiments, from the earliest to the most
recent ones. The accuracy of these experiments has helped us to estimate the
parameters of the cosmological model with unprecedented precision so that in
the future we shall be able to test not only cosmological models but General
Relativity itself on cosmological scales.
