Animal development requires a carefully orchestrated cascade of cell fate specification events and cellular movements. A surprisingly small number of choreographed cellular behaviours are used repeatedly to shape the animal body plan. Among these, cell intercalation lengthens or spreads a tissue at the expense of narrowing along an orthogonal axis. Key steps in the polarization of both mediolaterally and radially intercalating cells have now been clarified. In these different contexts, intercalation seems to require a distinct combination of mechanisms, including adhesive changes that allow cells to rearrange, cytoskeletal events through which cells exert the forces needed for cell neighbour exchange, and in some cases the regulation of these processes through planar cell polarity.