  The aim of this paper is to study codimension one foliations on rational
homogeneous spaces, with a focus on the moduli space of foliations of low
degree on Grassmannians and cominuscule spaces. Using equivariant techniques,
we show that codimension one degree zero foliations on (ordinary, orthogonal,
symplectic) Grassmannians of lines, some spinor varieties, some Lagrangian
Grassmannians, the Cayley plane (an $E_6$-variety) and the Freudenthal variety
(an $E_7$-variety) are identified with restrictions of foliations on the
ambient projective space. We also provide some evidence that such results can
be extended beyond these cases.
