The rapid development of computer technology in the last decades provided scientists with new opportunities to expand their research fields and in the same time to compress the necessary time to obtain research based scientific conclusions. This fast tendency also significantly affected the scientific discovery trend, and in many research fields we observe a transition from standard laboratory experiments to numerical experiments. In the particular research field of Earth Sciences, computational modeling constitutes a powerful predictive tool that fills a geological and geophysical data gap. The geological record covers well the Earth’s surface but is quite limited in depth, whereas geophysical information can provide depth-based information but it is limited in time to present day. Therefore, there is a large data gap in time and space that cannot be covered unless some indirect and intuitive prediction method is used. In this picture, numerical simulations come as an essential research tool. In this work, we provide a review about the research progress obtained in the last 15 years using high-performance computing at the Computational Geodynamics Laboratory at the Centro de Geociencias, Universidad Nacional Autónoma de México.