The world is shifting to electric vehicles to mitigate climate change. Here, we quantify the future demand for key battery materials, considering potential electric vehicle fleet and battery chemistry developments as well as second-use and recycling of electric vehicle batteries. We find that in a lithium nickel cobalt manganese oxide dominated battery scenario, demand is estimated to increase by factors of 18-20 for lithium, 17-19 for cobalt, 28-31 for nickel, and 15-20 for most other materials from 2020 to 2050, requiring a drastic expansion of lithium, cobalt, and nickel supply chains and likely additional resource discovery. However, uncertainties are large. Key factors are the development of the electric vehicles fleet and battery capacity requirements per vehicle. If other battery chemistries were used at large scale, e.g. lithium iron phosphate or novel lithium-sulphur or lithium-air batteries, the demand for cobalt and nickel would be substantially smaller. Closed-loop recycling plays a minor, but increasingly important role for reducing primary material demand until 2050, however, advances in recycling are necessary to economically recover battery-grade materials from end-of-life batteries. Second-use of electric vehicles batteries further delays recycling potentials.