Crustal movement information with millimeter-scale measurement accuracy, obtained through synthetic aperture radar interferometry (InSAR) technology, is crucial for assessing the seismic risk of active faults. This technology involves several fields, such as earthquake geology, geophysics, geodesy, and remote sensing. Thus, researchers from various fields need to acquire a foundational understanding of the necessary professional knowledge when applying this technique. This paper first systematically presents an introduction to the basic knowledge of seismology and geophysics, including active faults and earthquakes. Given the unique characteristics of crustal deformation monitoring using radar satellites, the paper then discusses the satellite observation geometry and explains the conversion between line-of-sight deformation and three-dimensional crustal movement/fault movement. The paper also highlights the limitations of space-borne InSAR technology in monitoring strike-slip fault movements with varying strike orientations. The inversion methods for estimating slip rates of active faults using deformation profiles were summarized. These methods include the screw dislocation model (SDM) and earthquake cycle model for strike-slip faults, the edge dislocation model for dip-slip (normal/thrust) faults, as well as the variants of the SDM that include other factors, such as the asymmetric and shallow creep models. These analytical and semi-analytical models have been widely used in the study of active faults due to their simplicity, ease of implementation, and high accuracy. Finally, the paper discusses the influence of non-tectonic signals in the InSAR deformation field and highlights the problems that need attention in practical applications. This work provides valuable insights for readers to better understand the current methods and knowledge related to monitoring active fault movement using InSAR. The findings are of considerable value for earthquake prevention and disaster reduction efforts, such as regional earthquake risk analysis.