The CDF and D0 experiments at the Tevatron ppbar collider have pioneered and established the role of flavor physics in hadron collisions. A broad program is now at its full maturity. We report on three new results sensitive to physics beyond the standard model, obtained using the whole CDF dataset: a measurement of the difference of CP asymmetries in K+K− and π+π− decays of D0 mesons, new bounds on the B0s mixing phase and on the decay width difference of B0s mass-eigenstates, and an update of the summer 2011 search for B0(s) mesons decaying into pairs of muons. Finally, the D0 confirmation of the observation of a new hadron, the χb(3P) state, is briefly mentioned.