At low temperatures, conduction electrons in disordered metals maintain quantum phase coherence over times often exceeding one nanosecond — several orders of magnitude longer than the time between elastic collisions. Phase coherence is broken by inelastic collisions, which also relax the energy distribution of the electrons toward thermal equilibrium. Theory predicts that the phase coherence time should increase as the temperature is lowered, whereas many experiments show a saturation of the phase coherence time at temperatures below 1 K. The issue of whether those observations reflect a fundamental, intrinsic decoherence mechanism, or an extrinsic, sample-dependent source of decoherence has been controversial. I will discuss experiments that measure the electron phase coherence time and others that measure the (closely related) rate of inelastic energy exchange between electrons. By studying the effects of an applied magnetic field on these two kinds of experiments, we have learned that very dilute magnetic impurities can dominate both electron decoherence and energy exchange, even at concentrations less than one part per million.