Since the first ruby laser was invented, researchers have focused their attention on how to achieve a strong laser light source, which cannot be produced by the ordinary light sources. Since then, the rich and colorful characteristics of nonlinear optical materials have been discovered, such as the saturation absorption, reverse saturation absorption and nonlinear refraction. They are applied to optoelectronic devices, optical switching devices and optical communication. At the same time, with the increase of the requirements for device integration performance in industrial production, ordinary three-dimensional devices are difficult to meet the production requirements, and the advent of low-dimensional semiconductor devices effectively solves this problem. Therefore, the combination of nonlinear optics and low-dimensional semiconductor materials is a general trend. The emergence of quantum dots, quantum wire lasers, and amplifiers confirms this. In this paper, we summarize the frontier work on nonlinear optics by selecting several special low-dimensional structures and several materials, providing some references for future research. However, due to the fact that the instability and low filling ratio of low-dimensional materials remain to be improved, further relevant research is still required.