We report the discovery of novel CO2-based networks stabilized by Li+ cations in solid-state phases. Our exploration of the energy landscape of the Li-CO2 binary phase diagram using ab initio evolutionary structure searches revealed that in addition to the well-characterized C2O42- oxalate in Li2C2O4 viable covalent CO2-based nets emerge upon compression within the 0-100 GPa pressure range. Novel molecular units are described, such as ethene-like C(2)O(4)(4- )in C2/m Li-2(CO2), finite C(4)O(8)(6-)chains in P(1) over-bar Li-3(CO2)(2), one-dimensional polymeric forms based on 1,4-dioxane rings in P2/c LiCO2, and the C(O-)(2) moieties in Pnma Li2CO2. This investigation shows the oxalate motif is maintained when the concentration of lithium increases from 1 to 2 in LixCO2; this interesting property may have potential in the development of renewable Li-ion batteries. Moreover, a variety of metastable phases were predicted, such as the covalent CO2-based layer in P(1) over-bar Li(CO2)(2).