  We describe a method to couple Z' gauge bosons to the standard model (SM),
without charging the SM fields under the U(1)', but instead through effective
higher dimension operators. This method allows complete control over the
tree-level couplings of the Z' and does not require altering the structure of
any of the SM couplings, nor does it contain anomalies or require introduction
of fields in non-standard SM representations. Moreover, such interactions arise
from simple renormalizable extensions of the SM - the addition of vector-like
matter that mixes with SM fermions when the U(1)' is broken. We apply effective
Z' models as explanations of various recent anomalies: the D0 same-sign dimuon
asymmetry, the CDF W+di-jet excess and the CDF top forward-backward asymmetry.
In the case of the W+di-jet excess we also discuss several complementary
analyses that may shed light on the nature of the discrepancy. We consider the
possibility of non-Abelian groups, and discuss implications for the
phenomenology of dark matter as well.
