The Cosmic Microwave Background (CMB) is a relict of the early universe. Its perfect 2.725K blackbody
spectrum demonstrates that the universe underwent a hot, ionized early phase; its anisotropy (about 80 µK rms)
provides strong evidence for the presence of photon-matter oscillations in the primeval plasma, shaping the initial
phase of the formation of structures; its polarization state (about 3 µK rms), and in particular its rotational
component (less than 0.1 µK rms) might allow to study the inflation process in the very early universe, and the
physics of extremely high energies, impossible to reach with accelerators. The CMB is observed by means of
microwave and mm-wave telescopes, and its measurements drove the development of ultra-sensitive bolometric
detectors, sophisticated modulators, and advanced cryogenic and space technologies. Here we focus on the new
frontiers of CMB research: the precision measurements of its linear polarization state, at large and intermediate
angular scales, and the measurement of the inverse-Compton effect of CMB photons crossing clusters of Galaxies.
In this framework, we will describe the formidable experimental challenges faced by ground-based, near-space and
space experiments, using large arrays of detectors. We will show that sensitivity and mapping speed improvement
obtained with these arrays must be accompanied by a corresponding reduction of systematic effects (especially
for CMB polarimeters), and by improved knowledge of foreground emission, to fully exploit the huge scientific
potential of these missions.