In this report I review recent results in the field of rare
decays at the Tevatron CDF II and D0 experiments.  The presentation is
focused on rare decays of charm and bottom mesons with two muons in the
final state.  This includes improvements over the previously available
limits on the following branching ratios: B(D+ --> pi++ mu+ mu-) < 4.7 x
10-6, B(B0(s) --> phi mu+ mu-) < 3.2 x 10-6, B(B)_s --> mu+ mu-) < 1 x
10-7, and B(B0(d) --> mu+ mu-) < 3 x 10-8 all at the 90% confidence
level.  Also reported are the first direct observation of D+_s --> phi
pi++ --> mu+ mu- pi++ with a significance above background of over 7
standard deviations and evidence of D+ --> phi pi++ --> mu+ mu- pi++ with a
significance of 3.1 and B(D+ --> phi pi++ --> mu+ mu- pi++) = (1.75 +/- 0.7
+/- 0.5) x 10-6.