The cosmic microwave background and its polarization

The DASI discovery of CMB polarization, confirmed by WMAP, has opened a new chapter in cosmology. Most of the useful information about inflationary gravitational waves and reionization is on large angular scales where Galactic foreground contamination is the worst. The goal of the present review is to provide the state-of-the-art of the CMB polarization from a practical point of view, connecting real-world data to physical models. We present the physics of this polarized phenomena and illustrate how it depends of various cosmological parameters for standard adiabatic models. We also present all observational constraints to date and discuss how much we have learned about polarized fore-grounds so far from the CMB studies. Finally, we comment on future prospects for the measurement of CMB polarization.