In recent years, a critical need has emerged to accelerate innovation of energy storage devices with the goal of improving device performance (energy and power), safety, and reliability for diverse applications ranging from vehicle electrification to renewable energy integration and grid storage. Lithium-ion batteries, for example, are leading the race for electric drive vehicles, while alternative chemistries like sodium-ion batteries are receiving renewed attention for grid applications. A commonality among these energy storage devices is that they are complex, dynamic systems composed of mixed functional materials. These materials support a multitude of coupled physicochemical processes encompassing electronic, ionic, and diffusive transport in electrode and electrolyte phases, electrochemical and phase-change reactions, and stress generation in multiscale porous electrodes. The performance and lifetime of such electrochemical energy storage devices are therefore dependent on complex reaction and transport processes spanning across multiple length and time scales. Continued improvement of electrochemical energy storage devices for vehicle electrification, renewable energy integration, and grid storage depends on understanding the underlying multiscale, multiphysics processes. Computational models and characterization of mechanical, thermal, and electrochemical processes play an important role in providing insight into coupled multiphysics interactions.