Electrochemical energy storage devices are becoming increasingly important to our global society, and polymer materials are key components of these devices. As the demand for high-energy density devices increases, innovative new materials that build on the fundamental understanding of physical phenomena and structure–property relationships will be required to enable high-capacity next-generation battery chemistries. In this Review, we discuss core polymer science principles that are used to facilitate progress in battery materials development. Specifically, we discuss the design of polymeric materials for desired mechanical properties, increased ionic and electronic conductivity and specific chemical interactions. We also discuss how polymer materials have been designed to create stable artificial interfaces and improve battery safety. The focus is on these design principles applied to advanced silicon, lithium-metal and sulfur battery chemistries.