The features of spin, charge and orbital orderings in the cobaltites

Complex cobalt oxides known as cobaltites are reviewed, including $Ln_2\mathrm{Co}\mathrm{O}_3$-based perovskite-structured rare-earth cobaltites (where $Ln$ is lanthanum or a lanthanide), quasi-two and quasi-one-dimensional cobaltites of the types $Ln\mathrm{Co}_2\mathrm{O}_{5+\delta}$, $Ln\mathrm{Co}\mathrm{O}_4$ and $\mathrm{Ca}_3\mathrm{Co}_2\mathrm{O}_8$, and the superconducting compounds $\mathrm{Na}_x\mathrm{Co}\mathrm{O}_2\cdot y\mathrm{H}_2\mathrm{O}$. Key experimental and theoretical results are presented, with emphasis on the interplay between charge, spin, and orbital degrees of freedom. Two problems of specific relevance to cobaltites — the spin state instability of $\mathrm{Co}^{3+}$ ions in $Ln\mathrm{Co}\mathrm{O}_3$ and the nature of superconductivity in $\mathrm{Na}_x\mathrm{Co}\mathrm{O}_2\cdot y\mathrm{H}_2\mathrm{O}$ — are also given significant attention.