Bending the rules: curvature's impact on cell biology

Curvature is a ubiquitous feature in biology, shaping structures at every scale and playing diverse roles in processes ranging from membrane dynamics to tissue organization. In this review, we first introduce briefly the fundamental concepts and mathematical principles of curvature. The second section explores how membrane curvature is perceived by molecular sensors and integrated into cellular responses. The third section examines the effects of curvature on cellular processes and behaviors at the cell-scale, providing a detailed discussion of the underlying mechanisms. Finally, we offer insights into emerging perspectives and highlight the future challenges in unraveling the multifaceted roles of curvature in biology.