In capacitive deionization (CDI), water is desalinated by storing ions in electrical double layers (EDLs) within the micropores of charged porous carbon electrodes. Recent experiments using chemically modified electrodes have shown differing, novel phenomena such as “inverted CDI,” “enhanced CDI,” and “inversion peaks.” We here present an EDL and dynamic model which includes immobile chemical charge in the micropores and show that the models predict these disparate experimental observations. Our model also makes predictions for a previously undiscovered operational regime with higher salt adsorption, which we term extended voltage CDI.