The evolution of future communication technologies towards higher carrier frequencies is inevitable to meet the escalating demands for data transmission rates. The terahertz(THz) spectrum emerges as a critical enabler for communication systems characterized by high stability and rapid data transfer rates. This paper reviews research progress on terahertz near-field channel characteristics and channel modeling. Firstly, the necessity of near-field channel analysis in the terahertz frequency band is introduced, the difference between near and far field channels is compared, and the spherical wavefront modeling and the model based on electromagnetic wave theory are introduced. Secondly, combining the channel modeling technology and the characteristics of the near-field channel, the methodology that can be used in near-field channel modeling is presented. Finally, the paper encapsulates the findings on terahertz near-field channel characteristics and offers insights into potential future research.