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Solid inorganic and polymeric electrolytes have the potential to enable rechargeable batteries with higher energy densities, compared to current lithium-ion technology, which uses liquid electrolyte. Inorganic materials such as ceramics and glasses conduct lithium ions well, but they are brittle, which makes incorporation into a battery difficult. Polymers have the flexibility for facile use in a battery, but their transport properties tend to be inferior to inorganics. Thus, there is growing interest in composite electrolytes with inorganic and organic phases in intimate contact. This article begins with a discussion of ion transport in single-phase electrolytes. A dimensionless number (the Newman number) is presented for quantifying the efficacy of electrolytes. An effective medium framework for predicting transport properties of composite electrolytes containing only one conducting phase is then presented. The opportunities and challenges presented by composite electrolytes containing two conducting phases are addressed. Finally, the importance and status of reaction kinetics at the interfaces between solid electrolytes and electrodes are covered, using a lithium-metal electrode as an example.