  We generalize Bestvina's notion of a $\mathcal{Z}$-boundary for a group to
that of a "coarse $\mathcal{Z}$-boundary." We show that established theorems
about $\mathcal{Z}$-boundaries carry over nicely to the more general theory,
and that some wished-for properties of $\mathcal{Z}$-boundaries become theorems
when applied to coarse $\mathcal{Z}$-boundaries. Most notably, the property of
admitting a coarse $\mathcal{Z}$-boundary is a pure quasi-isometry invariant.
In the process, we streamline both new and existing definitions by introducing
the notion of a "model $\mathcal{Z}$-geometry." In accordance with the existing
theory, we also develop an equivariant version of the above -- that of a
"coarse $E\mathcal{Z}$-boundary."
