'The Forms of Tissues, or Cell-aggregates': D'Arcy Thompson's influence and its limits

In two chapters of his book On Growth and Form, D'Arcy Thompson used numerous biological and physical observations to show how principles from mathematics and physics - such as pressure differences, surface tension and viscosity - could explain cell shapes and packing within tissues. In this Review, we depict influences that enabled the genesis of his ideas, report examples of his visionary observations and trace his impact over the past 100 years. Recently, his ideas have been revisited as a new field of research emerged, linking cell-level physics with epithelial tissue structure and development. We critically discuss the potential and the limitations of both Thompson's and the modern approaches.