Ion separations are important for resource recovery, water treatment, and energy production and storage. Techniques such as chemical precipitation, selective adsorption, and solvent extraction are effective, but membranes may separate ions continuously with less waste and lower energy costs. Separation of monovalent and multivalent ions with nanofiltration or electrodialysis membranes already enables water softening and edible salt purification. Similar membranes are attractive as separators in vanadium redox flow batteries. Selective partitioning of divalent counter-ions into ion-exchange membranes even allows transport of these ions against their concentration gradients in salt mixtures. However, separations of ions with the same charge is more challenging. Recent research demonstrated highly selective ion "sieving" at small scales. Separations using electrical potentials and differences in ion electrophoretic mobilities are promising, but relatively unexplored. Carrier-mediated transport affords high selectivity in liquid membranes, but these systems are not very stable, and selective transport via hopping between anchored carriers has proven elusive. Finally, this paper discusses how concentration polarization decreases selectivities in many membrane processes. Although development of selective, inexpensive ion-separation membranes is a work in progress, successes in water softening and edible salt purification suggests that future selective membranes will serve as complementary methods to traditional purification techniques.