The D0 and CDF detectors at the Fermilab Tevatron have each accumulated more that 9 fb{sup -1} of integrated luminosity. The corresponding large datasets enable the two experiments to perform unprecedented studies of heavy flavor hadron properties. We present recent D0 and CDF measurements, focusing on rare decays and CP violation in B-meson decays. Flavor Physics probes new phenomena by either searching for small deviations from the Standard Model (SM) based theoretical predictions or by measuring quantities which are highly suppressed within the SM. Searching for small deviations from the SM are performed using large strange, charm or bottom hadron samples, mostly by kaon experiments of B factories. Measurements of highly suppressed quant...