The discovery of proteins that recognize membrane curvature created a paradigm shift by suggesting that membrane shape may act as a cue for protein localization that is independent of lipid or protein composition. Here we review recent data on membrane curvature sensing by three structurally unrelated motifs: BAR domains, amphipathic helices and membrane-anchored proteins. We discuss the conclusion that the curvature of the BAR dimer is not responsible for sensing and that the sensing properties of all three motifs can be rationalized by the physicochemical properties of the curved membrane itself. We thus anticipate that membrane curvature will promote the redistribution of proteins that are anchored in membranes through any type of hydrophobic moiety, a thesis that broadens tremendously the implications of membrane curvature for protein sorting, trafficking and signaling in cell biology.