Invagination is the process of a surface folding in on itself to form a cavity, pouch or tube. In developmental biology, invagination of epithelial sheets occurs in many contexts during embryonic development. Invagination is critical for making the primitive gut during gastrulation in many organisms, forming the neural tube in vertebrates, and in the morphogenesis of countless organs and sensory structures. Models of invagination that have been most thoroughly studied include the ventral furrow in Drosophila melanogaster, neural tube formation, and gastrulation in many marine organisms. The cellular mechanisms of invagination vary from one context to another but at their core they involve changing the mechanics of one side of a sheet of cells such that this pressure induces a bend in the tissue.
The term, originally used in embryology, has been adopted in other disciplines as well.