The rapid, stable cycling of rechargeable batteries requires well-controlled phase transformations of the redox active materials in each electrode, between the charged and discharged states. In Li-ion batteries, common intercalation materials, such as graphite and iron phosphate, undergo phase separation (into Li-rich and Li-poor phases), which limits the power density and causes degradation. A general mathematical theory, supported by recent x-ray imaging experiments, will be presented that shows how phase separation can be controlled by electro-autocatalytic reactions. For Li-metal batteries, theoretical and experimental results will be presented for the stability of lithium electrodeposition, controlled by electrokinetic phenomena in charged porous separators.