  We consider contact foliations: objects which generalise to higher dimensions
the flow of the Reeb vector field on contact manifolds. We list a number of
properties of such foliations, and propose two conjectures about the
topological types of their leaves, both of which coincide with the classical
Weinstein conjecture in the case of contact flows. We give positive partial
results for our conjectures in particular cases -- when the holonomy of the
contact foliation preserves a Riemannian metric, for instance -- extending
already established results from the field of Contact Dynamics.
