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The Standard Model Effective Field Theory (SMEFT) encodes the observable short range effects of heavy new physics as the coefficients of higher dimensional operators. It spans a large parameter space of effects, nearly all of them flavorful, i.e. mediating interactions between different generations of the Standard Model fermion fields. I will describe recent (arXiv:2210.09316) and current work that uses an SU(3)^5 flavor decomposition to organize the parameter space of a generic SMEFT into phenomenologically relevant subsets. This organization also simplifies the running in the SMEFT, to the point that it is (semi)analytically soluble. An SU(3)^5 flavor decomposition may therefore be a useful tool for thinking more globally about the SMEFT.