Towards a resolution of the longstanding controversy regarding the existence of Cu-Li intermetallic compounds, we extensively investigate the phase stability of Cu-Li intermetallics with various possible stoichiometries at zero temperature and pressure using a global structure searching method. It is found that Cu-Li intermetallics can exist stably at atmospheric pressure, and three stable phases (Fmmm Cu1Li2, Fd (3) over barm Cu2Li1, and P (1) over bar Cu7Li1) are identified. Electronic structure analysis reveals that although they are metallic, covalent Cu-Cu and ionic Cu-Li bonds are found in the three structures. Moreover, the 3d states of copper atoms are mostly responsible for bond formations in the stable phases predicted. For all the predicted Cu-Li intermetallics, the effect of Cu concentration on structure, mechanical and thermodynamic properties are calculated systematically. It is found that the copper atoms in Cu-Li intermetallics trend to form covalent bonds, so more covalent bonds are formed as Cu content increases, leading to the increases in the elastic moduli, Vicker hardness and Debye temperature with Cu content on the whole. The Poisson's ratios of Cu-Li intermetallics vary in the range of 0.25 and 0.35, and most of Cu-Li intermetallics exhibit an excellent ductile property. The elastic anisotropy calculations suggest that all the Cu-Li intermetallics show anisotropic elasticity more or less, and the percentage anisotropy in compressibility is smaller than that in shear for each of the predicted Cu-Li compounds.