Theoretical descriptions of the three-dimensional spectroscopies are presented in this paper by calculating the associated nonlinear response function. Previously, the harmonic approximation with the Wick's theorem was used to obtain theoretical expression of the three-dimensional vibrational response function, by treating the mechanical and electrical anharmonicities perturbatively. However, the bath-induced memory effect and anharmonicity-induced frequency shift were not correctly taken into account by the previous theory. By incorporating the system-bath interaction properly, the general nonlinear response functions for the three-dimensional vibrational, vibrational-electronic, or electronic spectroscopies are obtained and discussed in detail. By using the resultant nonlinear response function, two-color vibrational photon echo, three-dimensional sum- and difference-frequency generation spectroscopies, and two-color infrared pump-probe spectroscopy are theoretically proposed.