The present disclosure generally relates to methods, systems, and devices for electrically purifying liquids containing species such as minerals, salts, ions, organics, and the like. One aspect of the invention provides methods of regenerating media within an electrical purification device, for example, exposing the media to one or more eluting solutions, and/or selectively desorbing ions, organics, and/or other species from the media by exposing the media to certain eluting conditions. In yet another aspect, methods of selectively removing one or more ions, organics, and/or other species from a liquid to be purified are provided, e.g., by selective removal of one or more ions, or organics, and the like from solution that can easily precipitate, and/or cause scaling or fouling to occur. In still another aspect, the invention provides a method of treating a solution containing ions, organics, and/or other species using an electrical purification apparatus in a continuous or semi-continuous fashion, while also performing regeneration of media contained within the apparatus.