We review predictions of the theory of leading twist nuclear shadowing for inclusive unpolarized and polarized deuteron structure functions [Formula: see text], [Formula: see text] and [Formula: see text] and for the tagged deuteron structure function [Formula: see text]. We analyze the possibility to extract the neutron structure function [Formula: see text] from electron–deuteron data and demonstrate that an account of leading twist nuclear shadowing leads to large corrections for the extraction of [Formula: see text] from the future deuteron collider data both in the inclusive and in the tagged structure function modes. We suggest several strategies to address the extraction of [Formula: see text] and to measure at the same time the effect of nuclear shadowing via the measurement of the distortion of the proton spectator spectrum in the semi-inclusive eD → e′NX process. We address the issue of the final state interactions in the eD → e′NX process and examine how they affect the extraction of [Formula: see text].