The time over which an electron can maintain its phase coherence at low temperatures is of fundamental importance in mesoscopic systems. The observability of many phenomena, such as the Aharonov Bohm effect, the universal conductance fluctuations, the weak localization correction to the conductance, persistent current in ringstructures and many more rely on a long enough phase coherence time. In disordered conductors and within the standard Fermi liquid picture, the phase coherence time is expected to diverge at zero temperature. However, most experiments show a saturating phase coherence time at low temperatures. This saturation has often been attributed to the presence of a small amount of magnetic impurities giving rise to the so-called Kondo effect. In this paper, we present a brief review of recent advances, both experimental and theoretical, in the understanding of dephasing by magnetic impurities in the framework of the Kondo effect.