Recent heavy flavor results from the Tevatron

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 $\pi^+\pi^-$ decays of $D^0$ mesons, new bounds on the $B^0_s$ mixing phase and on the decay width difference of $B^0_s$ mass-eigenstates, and an update of the summer 2011 search for $B^0_(s)$ mesons decaying into pairs of muons. Finally, the D0 confirmation of the observation of a new hadron, the $\chi_b(3P)$ state, is briefly mentioned.