This talk will describe the physics of driven nucleation and growth in battery materials. The resulting nonequilibrium pattern formation may be either reaction-limited or transport limited. Examples of the former include driven phase separation in Li-ion batteries, electrodeposition in Li-air batteries, and Li plating in Li-ion batteries, controlled by electro-autocatalysis and competing electrochemical reactions. Examples of the latter include stable electrodeposition in Li-metal batteries with charged porous separators, controlled by deionization shock waves.