  Measurements of Flavor Changing Neutral Current (FCNC) processes (rare
decays, flavor mixing) play a key role to pursue new physics beyond the
Standard Model. We present recent analysis results about some FCNC transitions
performed by CDF and D0 collaborations, including the first observation of the
B_s->phi mu^+mu^- mode, the forward-backward asymmetry measurement in B->K^(*)
mu^+mu^-, and updated measurements of B_s (B^0)->mu^+mu^-, using data
corresponding to integrated luminosities from 3.7/fb to 5/fb. We also show the
CDF/D0 combined measurement of the B_s mixing phase using 2.8/fb of data per
experiment.
