Volume-dependent total energies of Al, Li, and various intermetallic Al-Li compounds have been calculated by the first-principles full-potential linearized augmented-plane-wave (FLAPW) method. These values have been used to calculate Al-Li phase diagrams according to the cluster variation method in the tetrahedron approximation. Methods for performing lattice-parameter optimization and for including relaxation effects are presented. Truly first-principles-based phase diagrams for solid phases computed without any fitting parameters or empirical formulas are shown to exhibit a remarkable agreement with experimental data. Subsequently, some empirical equations for the free energy of the liquid and the vibrational entropy have been added to the first-principles results and striking similarities with experimental phase diagrams were obtained. Special attention has been paid to the metastable ${\mathrm{Al}}_{3}$Li phase and to the mechanical properties of Al-rich Al-Li alloys. Furthermore, the influence of relaxation and vibrational entropy are discussed.