The pericyclic reaction concept was developed by Woodward and Hoffmann 56 years ago, before accurate quantum mechanical calculations of organic reaction pathways were possible. Since then, computational methods such as density functional theory and coupled-cluster methods have been formulated, and computer speeds have increased a hundred trillion (10 11 )-fold. The subtleties and timings of bond formation in reactions have been established by high-accuracy quantum mechanical calculations. The field of pericyclic reactions has been enriched by understanding of the borderline between concerted pericyclic reactions and stepwise reactions. Higher-order pericyclic reactions, involving more than six electrons, have ambimodal transition states that can form two, three, or even four products. In addition, while only imagined in the last century, the fact that enzymes can catalyze many pericyclic reactions has been repeatedly established in the 21 st century, aided enormously by computational studies.