In recent years, with continuous social and economic development, there has been an increase in the scale of reservoir impoundment and underground industrial development activities. Consequently, induced or triggered seismicity is increasing, resulting in escalating damage losses. Therefore, the impact of industrial production behaviors on regional seismicity and the safe implementation of industrial production without causing earthquakes are important topics being discussed and closely monitored by the public and scientific research community. In this paper, we provide an overview of induced or triggered earthquakes, both domestic and international, and explore their causative mechanisms. Additionally, we summarize the methods commonly used to study induced or triggered earthquakes in academia, beginning with the governing equations. With the ongoing development of science and technology, numerical simulation will present unique advantages and become an important scientific tool for studying induced or triggered earthquakes. To date, both domestic and foreign researchers have conducted meaningful studies on induced earthquakes using numerical simulation methods. The physical mechanisms that trigger earthquakes will gradually be revealed, and measures for prevention and control will be improved. This work will effectively reduce the hazards caused by industrial production and other activities, thereby reducing the risk of triggering major earthquakes. However, there are still many challenges in numerical earthquake prediction. It not only requires a flawless physical mechanism and advanced calculation methods but also necessitates comprehensive observation and the establishment of an industrial production system.