To date, the role of transport and insertion of membrane in the control of membrane remodelling during cell and tissue morphogenesis has received little attention. In contrast, the contributions of cytoskeletal rearrangements and both intercellular and cell-substrate attachments have been the focus of many studies. Here, we review work from many developmental systems that highlights the importance of polarized membrane growth and suggests a general model for the role of endocytic recycling during cell morphogenesis. We also address how the spatio-temporal control of membrane insertion during development can account for various classes of tissue rearrangements. We suggest that tubulogenesis, tissue spreading and cell intercalation stem mostly from a remarkably small number of cell intrinsic surface remodelling events that confer on cells different modes of migratory behaviours.