In-situ stress plays a crucial role in governing various parameters such as the distribution of oil and gas accumulation zones, the fracture pattern of reservoirs, formation fracture pressure, and collapse pressure. Understanding the distribution characteristics of current in situ stress of reservoirs has significant implications for exploration and development of oil and gas. This paper focuses on the characterization methods for current in situ stress of oil and gas reservoirs, discussing the research progress in testing methods, computational approaches, numerical simulations, and seismic prediction methods. The results indicate that the testing method including the on-site testing method and the laboratory testing method offer the relatively high accuracy, but this method only provides point-specific magnitude and direction of current in situ stress. The Computational approaches can obtain continuous profiles of current in situ stress along individual wells. After using the testing method for calibration, we can obtain relatively accurate calculation results. The numerical method can predict current in situ stress over large areas, but it requires rigorous model setup, boundary definition, and parameter selection. The seismic prediction method also can predict broad distribution of current in situ stress, but this method is influenced by many factors and we had better apply this method in conjunction with other methods. In the future, engineers and researchers should innovate testing technologies and instruments, and establish models and processes for joint use of multiple methods, and explore the development of novel current in situ stress prediction models based on artificial intelligence and big data.