The present invention relates generally to the deionization of liquids through the use of electrodeionization methods and apparatuses. The apparatuses may be configured to produce purified liquids for use in analytical techniques such as ion chromatography, inductively coupled plasma mass spectrometry and atomic absorption spectroscopy, among others, and to provide continuous regeneration of the ion exchange materials. The apparatuses may be configured according to the desired levels of deionization for anions, cations, or both. Finally, methods are presented for various uses of the apparatus specifically claimed.