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.