In the thematic review dedicated to polyoxometalate (POM) chemistry published in Chemical Reviews in 1998, no contribution was devoted to theory. This is not surprising because computational modelling of molecular metal-oxide clusters was in its infancy at that time. Nowadays, the situation has completely changed and modern computational methods have been successfully applied to study the structure, electronic properties, spectroscopy and reactivity of POM clusters. Indeed, the progress achieved during the past decade has been spectacular and herein we critically review the most important papers to provide the reader with an almost complete perspective of the field.

In this review we summarise the quantum chemistry studies carried out by several groups over the last ten years on polyoxometalates, or polyoxoanions. This is an immense family of compounds made up of transition metal ions in their highest oxidation state and oxo ligands. The continuous progress of computers in general, and quantum chemistry software in particular, has enabled a number of topics in polyoxometalate chemistry to be studied from the electronic structure of the most representative polyoxometalate, the so-called Keggin anion, to the factors governing the inclusion complexes and the magnetism in reduced complexes.