Frequency-modulated continuous-wave (FMCW) light detection and ranging (LiDAR) has the advantages of noncontact measurements, resistance to ambient light interference, high resolution, and the ability to simultaneously determine speed and distance information. In recent years, it has been widely used in various fields, including aerospace, precision manufacturing, and autonomous driving. The ranging performance of FMCW LiDAR significantly depends on the sweep linearity of its light source, which is typically influenced by several factors, such as uneven stress stretching, temperature variations, and circuit noise. These factors decrease the ranging resolution and accuracy. The influence of light source nonlinearity in FMCW LiDAR is analyzed theoretically, and research progress in different types of nonlinearity correction techniques is presented. The characteristics, advantages, and disadvantages of each method are summarized to provide a reference for future research.