The present invention describes methods and systems for extracting, capturing, reducing, storing, sequestering, or disposing of carbon dioxide (C0.sub.2), particularly from the air. The CO.sub.2 extraction methods and systems involve the use of chemical processes. Methods are also described for extracting and/or capturing CO.sub.2 via exposing air containing carbon dioxide to a solution comprising a base--resulting in a basic solution which absorbs carbon dioxide and produces a carbonate solution. The solution is causticized and the temperature is increased to release carbon dioxide, followed by hydration of solid components to regenerate the base.