The crystal structures of Li1.2V3O8 and a lithiated product Li4.0V3O8 have been determined by single-crystal X-ray diffraction methods. The structure refinement of Li1.2V3O8 confirms that of Li1+xV3O8 (x almost-equal-to 0) reported by Wadsley thirty-six years ago. However, unlike Wadsley's data, the refinement of Li1.2V3O8 demonstrates that the lithium ions are distributed over two independent crystallographic sites. One lithium ion, Li(1), is octahedrally coordinated; the other, Li (2), has tetrahedral coordination. Lithiation of Li1.2V3O8 with n-butyllithium at room temperature displaces Li(1) through an octahedral face into a neighbouring octahedral site, whereas Li (2) shifts its position very slightly to adopt octahedral coordination. During lithiation, the packing of the oxygen-ion array is adjusted slightly to adopt an arrangement that approaches cubic-close-packing. The lithiated product Li4V3O8 has a defect rock salt structure. The structural data provide a greater insight into the discharge mechanism that occurs in Li/Li1+xV3O8 electrochemical cells.