We study - experimentally and theoretically - the energetics, structural changes, and charge flows during the charging and discharging processes for a new high-capacity cathode material, Li8ZrO6 (LZO), which we study both pure and yttrium-doped. We quantum mechanically calculated the stable delithiated configurations, the delithiation energy, the charge flow during delithiation, and the stability of the delithiated materials. We find that Li atoms are easier to extract from tetrahedral sites than octahedral ones. We calculate a large average voltage of 4.04 eV vs Li/Li+ for delithiation of the first Li atom in a primitive cell, which is confirmed by galvanostatic charge/discharge cycling data. Energy calculations indicate that topotactic delithiation is kinetically favored over decomposition into Li, ZrO2, and O2 during the charging process, although the thermodynamic energy of the topotactic reaction is less favorable. When one or two lithium atoms are extracted from a primitive cell of LZO, its volume and structure change little, whereas extraction of the third lithium greatly distorts the layered structure. The Li6ZrO6 and Li5ZrO6 delithiation products can be thermodynamically metastable to release of O2. Experimentally, materials with sufficiently small particle size for efficient delithiation and relithiation were achieved within an yttrium-doped LZO/carbon composite cathode that exhibited an initial discharge capacity of at least 200 mAh/g over the first 10 cycles, with 142 mAh/g maintained after 60 cycles. Computations predict that during the charging process, the oxygen ion near the Li vacancy is oxidized for both pure LZO and yttrium-doped LZO, which leads to a small-polaron hole. (Figure Presented).