The dramatic ingression of tissue sheets that accompanies many morphogenetic processes, most notably gastrulation, has been largely attributed to contractile circum-apical actomyosin 'purse-strings' in the infolding cells. Recent studies, however, including one in BMC Biology, expose mechanisms that rely less on actomyosin contractility of purse-string bundles and more on dynamics in the global cortical actomyosin network of the cells. These studies illustrate how punctuated actomyosin contractions and flow of these networks can remodel both epithelial and planarly organized mesenchymal sheets.