On 14th April 1917, Nature announced that it had received a new publication entitled “On Growth and Form” by D’arcy Wentworth Thompson. This book was Thompson’s vision of how mathematical and physical principles define the development and final form of biological structures and 100 years later it is a classic text for researchers who cross the traditional disciplinary boundaries between physics, mathematics and biology. Nature celebrates the centenary of the publication of “On Growth and Form” with the publication of some interdisciplinary research and supporting comment pieces reflecting evolving fields in biophysics and applied mathematics. We also present an online collection of research and comment reflecting the diversity of research activity which crosses boundaries between the physical and biological sciences in developing our understanding of morphogenesis in its broadest sense. We hope you enjoy the collection.