  We develop some basic results in a higher dimensional foliated Mori theory,
and show how these results can be used to prove a structure theorem for the
Kleiman-Mori cone of curves in terms of the numerical properties of
$K_{\mathcal{F}}$ for rank 2 foliations on threefolds. We also make progress
toward realizing a minimal model program for rank 2 foliations on threefolds.
