Helical modes, in which the momentum and spin quantum numbers are strongly coupled, have recently appeared in the front line of one-dimensional physics through the discovery of materials exhibiting the quantum spin-Hall effect. The fascinating conduction properties of the edge states of such materials is determined not just by the naturally strongly correlated nature of one-dimensional quantum systems, but also through the helical nature of such modes. In this presentation, I will consider two examples of helical modes. The first arises in the edge states of the quantum spin-Hall effect, where I will consider how the helical structure of the states influences the Kondo effect when one traps a single spin within a double constriction. The second example appears when domain walls are induced into the quantum Hall state of bilayer graphene under appropriate gating. I will demonstrate that one-dimensional helical modes form on this kink, which may then be tuned through a quantum phase transition in the Z_2 universality class. The helical nature of the modes means the two phases on either side of this transition have distinct conducting properties, in particular one is superfluid and the other is insulating. References: C.-W. Huang, S.T. Carr, D. Gutman, E. Shimshoni and A.D. Mirlin, PRB 88, 125134 (2013) V. Mazo, C.-W. Huang, E. Shimshoni, S.T. Carr and H.A. Fertig, arXiv:1309.1563