Heavy vectorlike quarks (VLQs) appear in many models of beyond the Standard Model physics. Direct experimental searches require these new quarks to be heavy, ≳800–1000  GeV. We perform a global fit of the parameters of simple VLQ models in minimal representations of SU(2)L to precision data and Higgs rates. An interesting connection between anomalous Zbb¯ interactions and Higgs physics in VLQ models is discussed. Finally, we present our analysis in an effective field theory (EFT) framework and show that the parameters of VLQ models are already highly constrained. Exact and approximate analytical formulas for the S and T parameters in the VLQ models we consider are available in the Supplemental Material as Mathematica files.