  Transition metal oxides whose lattice structure has edge-sharing network of
octahedra constitute a diverse group of intriguing materials besides compounds
with corner-sharing octahedra such as perovskites. We present a theoretical
investigation of the interplay among spin, orbital and lattice degrees of
freedom in these materials. We focus on $t_{2g}$ electron systems where a keen
competition among those degrees of freedom is expected to emerge under a
relatively weak Jahn-Teller coupling. We study the interplay between spin and
orbital degrees of freedom in vanadium spinels and titanium pyroxenes. We
clarify the important role of the strong anisotropy in the orbital interactions
due to the edge-sharing geometry. We also discuss the interplay between spin
and lattice in chromium spinels focusing on the magnetization process under the
external magnetic field.
