  I review recent observations of molecular gas in the halo of the Milky Way
and in the Magellanic Clouds. Far-ultraviolet absorption line studies of
molecular hydrogen (H_2) with ORFEUS and FUSE have unveiled the presence of a
diffuse molecular hydrogen component in intermediate- and high-velocity clouds
in the Galactic halo. Although the number of measurements is still quite small,
the data suggests that diffuse H_2 in the halo exists only in clouds that
contain a sufficient amount of heavy elements and dust, on whose surface the
H_2 formation proceeds most efficiently. The implications of these observations
for our understanding of the Milky Way halo are discussed.
