Transition metal oxides containing 4d and 5d elements have recently attracted much attention due to new phenomena arising from the interplay of strong correlations and spin-orbit coupling. Of a particular interest are Mott insulators based on ions with four valence electrons occupying t_2g orbitals. These may host an unusual magnetism based on a dynamic mixing of low-energy ionic states via exchange processes. The particular set of exchange processes involving these states depends on the lattice geometry and the available hopping channels, giving rise to models with very distinct properties. In the talk, I will give a brief overview of the various possibilities that may be encountered, focusing on the corresponding phase diagrams and rather peculiar excitation spectra. In more detail, I will discuss a scenario for a possible realization of the well-known transverse-field Ising model.