  We derive an {\em ab initio} $\pi$-band tight-binding model for $AB$ stacked
bilayer graphene based on maximally localized Wannier wave functions (MLWFs)
centered on the carbon sites, finding that both intralayer and interlayer
hopping is longer in range than assumed in commonly used phenomenological
tight-binding models. Starting from this full tight-binding model, we derive
two effective models that are intended to provide a convenient starting point
for theories of $\pi$-band electronic properties by achieving accuracy over the
full width of the $\pi$-bands, and especially at the Dirac points, in models
with a relatively small number of hopping parameters. The simplified models are
then compared with phenomenological Slonczewski-Weiss-McClure type
tight-binding models in an effort to clarify confusions that exists in the
literature concerning tight-binding model parameter signs.
