Bacteria and eukaryotic cells contain geometry-sensing tools in their cytosol: protein motifs or domains that recognize the curvature, concave or convex, deep or shallow, of lipid membranes. These sensors contrast with classical lipid-binding domains by their extended structure and, sometimes, counterintuitive chemistry. Among the sensors are long amphipathic helices, such as the ALPS motif and the N-terminal region of α-synuclein, whose apparent "design defects" translate into a remarkable ability to specifically adsorb to the surface of small vesicles. Fundamental differences in the lipid composition of membranes of the early and late secretory pathways probably explain why some sensors use mostly electrostatics whereas others take advantage of the hydrophobic effect. Membrane curvature sensors help to organize very diverse reactions, such as lipid transfer between membranes, the tethering of vesicles at the Golgi apparatus, and the assembly-disassembly cycle of protein coats.