  Heavy vector-like quarks (VLQs) appear in many models of beyond the Standard
Model physics. Direct experimental searches require these new quarks to be
heavy, $\gsim$ 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 $Z b {\overline {b}}$
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 posted at
https://quark.phy.bnl.gov/Digital_Data_Archive/dawson/vlq_17/ as Mathematica
files.
