In a wide range of epithelial tissues such as kidney tubules or breast acini, cells organize into bidimensional monolayers experiencing an out-of-plane curvature. Cancer cells can also migrate collectively from epithelial tumors by wrapping around vessels or muscle fibers. However, in vitro experiments dealing with epithelia are mostly performed on flat substrates, neglecting this out-ofplane component. In this paper, we study the development and migration of epithelial tissues on glass wires of well-defined radii varying from less than 1 μm up to 85 μm. To uncouple the effect of out-of-plane curvature from the lateral confinement experienced by the cells in these geometries, we compare our results to experiments performed on narrow adhesive tracks. Because of lateral confinement, the velocity of collective migration increases for radii smaller than typically 20 μm. The monolayer dynamics is then controlled by front-edge protrusions. Conversely, high curvature is identified as the inducer of frequent cell detachments at the front edge, a phenotype reminiscent of the Epithelial−Mesenchymal Transition. High curvature also induces a circumferential alignment of the actin cytoskeleton, stabilized by multiple focal adhesions. This organization of the cytoskeleton is reminiscent of in vivo situations such as the development of the trachea of the Drosophila embryo. Finally, submicron radii halt the monolayer, which then reconfigures into hollow cysts.collective cell behaviors | out-of-plane curvature | epithelial tubes