Redox-flow batteries can, in principle, use a wide range of active materials. However, a number of simultaneous requirements must be met to make a chemistry attractive. One of the most challenging requirements is minimizing transport of active species through the membrane separating the positive and negative electrodes, and the ensuing inefficiency and capacity loss. Developing technologies to mitigate crossover, and strategies for recovering from its consequences, will enable development of successful systems with new active materials. The rate and impact of crossover depend on the nature of the active materials and their fate after they transport across the separator. Accordingly, electrolyte solutions can be classified by what happens to the active species at the opposing electrolyte. This behavior also dictates what recovery strategies may be employed, and at what frequency. This review describes desirable attributes for active materials and separators that help diminish crossover, and strategies that can be used to recover from its effects for each of the different classes of electrolytes.