Precisely controlled cell deformations are key to cell migration, division and tissue morphogenesis, and have been implicated in cell differentiation during development, as well as cancer progression. In animal cells, shape changes are primarily driven by the cellular cortex, a thin actomyosin network that lies directly underneath the plasma membrane. Myosin-generated forces create tension in the cortical network, and gradients in tension lead to cellular deformations. Recent studies have provided important insight into the molecular control of cortical tension by progressively unveiling cortex composition and organization. In this Cell Science at a Glance article and the accompanying poster, we review our current understanding of cortex composition and architecture. We then discuss how the microscopic properties of the cortex control cortical tension. While many open questions remain, it is now clear that cortical tension can be modulated through both cortex composition and organization, providing multiple levels of regulation for this key cellular property during cell and tissue morphogenesis.