This document describes the LEST vector polarimeters for the visible and the near-infrared part of the solar spectrum. After some general remarks on precise polarimetry with large telescopes, the authors present the specifications based on scientific reasons and some general design considerations. The proposed instrument design for the visible is based on the ZIMPOL II concept. They present two different concepts for vector polarimetry in the near infrared. One is based on a beam-splitter system combined with liquid crystal modulators, while the other is based on the same modulator package as used in the visible and optical demodulation in the final focus.