The Standard Model Effective Field Theory (SMEFT) provides a consistent framework for comparing precision measurements at the LHC to the Standard Model. The observation of statistically significant non-zero SMEFT coefficients would correspond to physics beyond the Standard Model (BSM) of some sort. A more difficult question to answer is what, if any, detailed information about the nature of the underlying high scale model can be obtained from these measurements. In this work, we consider the patterns of SMEFT operators present in five example models and discuss the assumptions inherent in using global fits to make BSM conclusions. We find that including renormalization group effects has a significant impact on the interpretation of the results. As a by-product of our study, we present an up-dated global fit to SMEFT coefficients in the Warsaw basis including some next-to-leading order QCD corrections in the SMEFT theory.