Designing materials for electrochemical energy storage with short charging times and high charge capacities is a longstanding challenge. The fundamental difficulty lies in installing a high density of redox couples into a stable material that can efficiently conduct both ions and electrons. Here, we report all-organic, fused aromatic materials that store up to 310 mAh g–1 and charge in as little as 33 seconds. This performance stems from abundant quinone/imine functionalities that act as redox-active sites, engage in hydrogen bonding for outstanding stability upon cycling, and enable bulk electronic delocalization for high-rate energy storage. The hydrogen bonding-assisted bulk charge storage here contrasts with the surface-confined or hydration-dependent behavior of traditional inorganic electrodes. These materials outperform state-of-the-art faradaic and capacitive electrodes in both capacity and power capability.