•Computational methods applied on flavonoids have been described and discussed.•Computational chemistry is an helpful tool to understand the chemistry of flavonoids.•Theoretical calculations result accurate in describing the properties of anthocyanins.•Hybrid functionals have been successfully applied to anthocyanidins and anthocyanins.•Metal chelation and co-pigmentation have been computationally described. Anthocyanins and anthocyanidins are polyphenolic compounds, responsible for the red and blue colours in several fruits, flowers, and leaves. Their colorant properties, bioavailability and antioxidant activity, made anthocyanins and anthocyanidins largely adopted in food and pharmaceutical industries. In this body of work, we firstly introduced structure, photophysical properties, co-pigmentation, antioxidant properties, glycosylation and complexation of anthocyanins and anthocyanidins. Secondly, we reported the computational methods adopted and the main theoretical results involving either anthocyanins and anthocyanidins, ranging from the first theoretical investigation on the structure of flavylium ions to the most recent studies on anthocyanins adsorbed on TiO2. We reviewed the computational contributions to the description of molecular properties of anthocyanins and anthocyanidins, giving a particular attention to the geometries, the spectroscopic features and the complexation properties of such molecules. Nowadays, theoretical calculations represent an essential methodology to understand and predict the chemical and physical properties of anthocyanins and their derivates.