The third-order nonlinear optical effect is a fundamental phenomenon with extensive applications in laser wavelength extension, modulation, and spectral analysis. Direct third-harmonic generation(THG), as a typical third-order nonlinear process, can shorten the laser wavelength to 1/3 of the fundamental-wave and triple the photon energy. It enables great optical conversion from infrared light to short wavelengths (e.g., visible, ultraviolet, and vacuum ultraviolet region), thus enhancing laser device integration, facilitating high-performance electronic and optical components, and meeting the urgent demands for specific wavelengths in laser processing. Additionally, the inverse process of THG allows optical parametric down-conversion to generate multi-photon entangled states, thus aiding in high-efficiency and multi-dimensional quantum light sources for important applications, such as quantum key distribution and teleportation. Starting from the basic principles of THG, this paper analyzes the strict conditions of energy conservation and momentum conservation for THG process. We summary the development status of THG in bulk nonlinear crystals, topological semimetals, epsilon-near-zero thin films, and silicon-based metasurfaces. In addition, their THG wavelength ranges and conversion efficiencies are also compared in detail. Finally, we discuss the challenges for efficient direct THG in bulk nonlinear crystals and prospect their development trends in the future.