There is growing interest in the use of peptides as therapeutic drugs and, in particular, in the potential of cyclotides, a family of cyclic peptides with remarkable stability and amenability to sequence engineering, as scaffolds in drug design. As well as having an ultrastable structure, many natural cyclotides have intrinsic biological activities with potential pharmaceutical or agricultural applications. Some cyclotides also have the ability to cross membrane barriers and to enter into cells; in particular, cyclotides that belong to the Möbius and bracelet subfamilies have been found to harbor lipid-binding domains, which allow for the specific recognition of phosphatidylethanolamine phospholipids in biological membranes. This lipid selectivity is intimately correlated with the highly conserved three-dimensional structures of cyclotides and is important for their reported biological properties and cell penetration ability. The membrane binding features of Möbius and bracelet cyclotides contrast with the lack of membrane binding of trypsin inhibitor cyclotides, which have physicochemical properties and bioactivities different from those of the other two subfamilies of cyclotides but are also able to enter cells. This review discusses the structures of cyclotides with regard to their myriad of biological activities and describes the role of membrane binding in their functions and ability to enter cells.