Abstract: Multi-stage sedimentation and diagenetic processes lead to complex in situ stresses in subsurface hydrocarbon reservoirs. The in situ stresses have a broad magnitude range and their distribution directions are complicated, significantly impacting the rock physics properties and seismic propagation response in reservoirs. Seismic reflection and transmission (R/T) coefficient equations can quantify the relationship between reservoir properties and observed geophysical data. Therefore, seismic R/T coefficient equations considering the effects of in situ stresses can help to better understand the characteristics of wave propagation on deep-strata stratigraphic interfaces, laying a theoretical foundation for exploring deep-strata hydrocarbon. This research topic is attracting the attention of international scholars. Most reported stress-dependent wave R/T coefficient equations consider the infinitesimal deformations induced by the in situ stress and wave perturbation based on the theory of acoustoelasticity; these approaches have been preliminarily applied in several theoretical and practical scenarios such as seismic inversion for stress-induced anisotropy parameters, in situ stress detection, and discrimination of oil and gas reservoirs. In this paper, we introduce the main body of solid acoustoelasticity theory and the stress-dependent seismic R/T coefficient equations based on acoustoelasticity theory, along with their basic assumptions, preliminary applications, limitations, and prospects in seismic exploration.