Nondegenerate two-photon absorption is a nonlinear optical effect in which two photons with different energy are absorbed by a medium simultaneously, resulting in a single electron transition from ground state to excited state through an intermediate virtual state. Compared with the degenerate two-photon absorption coefficient, the absorption coefficient of nondegenerate two-photon absorption is increased by tens or even hundreds of times due to the intermediate resonance effect, so it has great potentials in many nonlinear optical applications. Firstly, the basic principle of two-photon absorption is introduced and the enhancement mechanism of non-degenerate two-photon absorption is explained in this paper. Secondly, the basic method of measuring two-photon absorption is introduced in detail. Thirdly, the reports on nondegenerate two-photon absorption of three-dimensional semiconductor materials and two-dimensional materials are reviewed. Finally, the application progress of infrared detection and imaging, two-photon fluorescence microscope, all-optical switch and optical modulation is summarized, and the future research in this field is summarized and prospected.