Today, due to the increasing recognition of the capabilities of machine learning and deep learning algorithms, the use of these algorithms is undergoing significant development. This ongoing evolution has led to the creation and enhancement of numerous algorithms and their variants. These advancements not only enhance the accuracy of algorithms but also pose challenges for researchers in terms of their understanding and utilization. The increasing capabilities of these algorithms have resulted in a dramatic rise in their utilization within seismic exploration. Among these, generative adversarial algorithms stand out due to their unique abilities and rapid progress, making them a crucial part of deep learning algorithms applied to various seismic exploration challenges. One notable characteristic of this algorithm is its high complexity and the existence of multiple variants. In this article, we aim to provide a comprehensive yet concise overview of generative adversarial algorithms, focusing on their theoretical foundations and mathematical underpinnings as they apply to seismic exploration. By doing so, we facilitate researchers’ initial understanding of this algorithm, allowing them to grasp its fundamentals before delving into its intricacies and more time-consuming aspects. This approach enables researchers to intelligently and purposefully explore the algorithm according to their specific goals.