The Theme Customization API allows developers to build customization settings and controls in WordPress themes. It utilizes panels, sections, settings, and controls. Panels group sections. Sections contain controls. Controls allow changing settings, which define what the controls change. WordPress themes since version 3.4 include default customization options. Developers can also create custom controls using classes like WP_Customize_Control and subclasses for specific control types. The API allows live previews of theme customizations.