Molecular Gas in the Galactic Halo and Beyond

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.