Polyarenes, or polycyclic aromatic hydrocarbons (PAHs), represent a ubiquitous and heavily studied type of compounds, appealing for their interesting spectroscopic, supramolecular, organometallic, and other properties. A major branch of research is concerned with polyarene anions: their electronic and structural properties, reactivity, aromaticity, and spectroscopy. This review describes the major role of computational investigations in complementing, explaining, and guiding experimental research, and thus providing invaluable contribution to our understanding of polyarene anions. The scope of this review focuses on polyarenes composed only from sp2-hybridized carbons and limits the discussion to the quantum-mechanical method of calculation. The topics covered include computation-assisted characterization; choice of methods; transformations induced by reduction, including anistropic charge redistributions, reorganization of bonding structure, flattening of curved polyarenes (buckybowls), and Jahn–Tel