Abstract
Epithelial invagination is a fundamental module of morphogenesis that iteratively occurs to generate the architecture of many parts of a developing organism. By changing the physical properties such as the shape and/or position of a population of cells, invagination drives processes ranging from reconfiguring the entire body axis during gastrulation, to forming the primordia of the eyes, ears and multiple ducts and glands, during organogenesis. The epithelial bending required for invagination is achieved through a variety of mechanisms involving systems of cells. Here we provide an overview of the different mechanisms, some of which can work in combination, and outline the circumstances in which they apply.This article is part of the themed issue 'Systems morphodynamics: understanding the development of tissue hardware'.