We survey the implications for new physics of the discrepancy between the LEP
measurement of $R_b$ and its Standard Model prediction. Two broad classes of
models are considered: ($i$) those in which new $Z\bbar b$ couplings arise at
tree level, through $Z$ or $b$-quark mixing with new particles, and ($ii$)
those in which new scalars and fermions alter the $Z \bbar b$ vertex at one
loop. We keep our analysis as general as possible in order to systematically
determine what kinds of features can produce corrections to $R_b$ of the right
sign and magnitude. We are able to identify several successful mechanisms,
which include most of those which have been recently been proposed in the
literature, as well as some earlier proposals (\eg\ supersymmetric models). By
seeing how such models appear as special cases of our general treatment we are
able to shed light on the reason for, and the robustness of, their ability to
explain $R_b$.