Many batteries, including the state-of-the-art Lithium-ion technology, use porous intercalation electrodes. In such electrodes, energy is stored in the form of ions intercalating in particles. The conventional approach to designing such electrodes relies on using the porous electrode theory to upscale particle-scale behavior to the electrode-scale response. In this talk, I will discuss unusual material effects that obfuscate such a connection and can considerably change the design guidelines. Understanding these effects is critical to building lithium-ion batteries for new applications like extreme fast charging and electric flight as well as enabling batteries with new intercalation hosts.