Quantum calculations (mainly DFT) and molecular dynamics are increasingly effective tools to evaluate the physico-chemical properties of natural and bio-inspired antioxidants. Thermodynamic parameters (mainly bond dissociation enthalpies (BDE) of the O-H phenolic bond) allowed an accurate prediction of the Free Radical Scavenging Capacity of natural and hemi-synthetic compounds. Based on the Transition State and the Marcus Theories (for atomand electron-transfers, respectively), kinetics was also evaluated providing a better prediction of the antioxidant behaviour in solution or in the organism. Also pro-oxidant effects have been studied including the oxidatively-induced dimerization capacity. In this case, thermodynamic and kinetic calculations explain regio- and stereo-selectivity. MD simulations have been performed to provide an accurate picture of the interaction between natural antioxidants (polyphenols and other π-conjugated derivatives) and lipid bilayer membranes. Molecular dynamics allows evaluation of the ability of these molecules to approach and penetrate the membrane, and to predict their "exact" location and orientation.