The cells of many embryonic tissues actively narrow in one dimension (convergence) and lengthen in the perpendicular dimension (extension). Convergence and extension are ubiquitous and important tissue movements in metazoan morphogenesis. In vertebrates, the dorsal axial and paraxial mesodermal tissues, the notochordal and somitic mesoderm, converge and extend. In amphibians as well as a number of other organisms where these movements appear, they occur by mediolateral cell intercalation, the rearrangement of cells along the mediolateral axis to produce an array that is narrower in this axis and longer in the anteroposterior axis. In amphibians, mesodermal cell intercalation is driven by bipolar, mediolaterally directed protrusive activity, which appears to exert traction on adjacent cells and pulls the cells between one another. In addition, the notochordal–somitic boundary functions in convergence and extension by ‘capturing’ notochordal cells as they contact the boundary, thus elongating the boundary. The prospective neural tissue also actively converges and extends parallel with the mesoderm. In contrast to the mesoderm, cell intercalation in the neural plate normally occurs by monopolar protrusive activity directed medially, towards the midline notoplate–floor–plate region. In contrast, the notoplate–floor–plate region appears to converge and extend by adhering to and being towed by or perhaps migrating on the underlying notochord. Converging and extending mesoderm stiffens by a factor of three or four and exerts up to 0.6 μN force. Therefore, active, force–producing convergent extension, the mechanism of cell intercalation, requires a mechanism to actively pull cells between one another while maintaining a tissue stiffness sufficient to push with a substantial force. Based on the evidence thus far, a cell–cell traction model of intercalation is described. The essential elements of such a morphogenic machine appear to be (i) bipolar, mediolaterally orientated or monopolar, medially directed protrusive activity; (ii) this protrusive activity results in mediolaterally orientated or medially directed traction of cells on one another; (iii) tractive protrusions are confined to the ends of the cells; (iv) a mechanically stable cell cortex over the bulk of the cell body which serves as a movable substratum for the orientated or directed cell traction. The implications of this model for cell adhesion, regulation of cell motility and cell polarity, and cell and tissue biomechanics are discussed.