Possibly no other class of organic or inorganic compounds displays more versatility than polyoxometalates (POMs) (or polyoxoanions) with respect to electronic and molecular structures, properties, and applications. POMs attract the attention of scientists from many fields, such as catalysis, materials science, and medicine. More recently, POMs have also attracted the interest of computational chemists. This article describes some of the most relevant electronic properties for several of the most representative heteropolyoxoanions, such as the so-called Keggin [XM₁₂O₄₀]ⁿ⁻, Dawson [X₂M₁₈O₆₂]^m−, and Preyssler [XP₅W₃₀O₁₁₀]^q− anions. Density functional theory (DFT) methods have proven to be useful for the rationalization of many properties of POMs. In this article we illustrate some of them, often using the simple language of molecular orbitals.