High pressure is an important route for synthesizing materials that cannot be obtained in ambient conditions. The process of new materials discovery applying high pressure can be significantly accelerated as demonstrated in recent research combining state-of-the-art simulation approaches and experimental techniques. With rapid developments in materials prediction algorithms and the explosion of supercomputing capacity, accelerated discovery of new materials based on computational data is attracting much research interest. Progress in this highly interdisciplinary research field is expected to have a long-term impact in materials, applications and devices. Different theoretical approaches have been shown to be effective in the search for materials with emergent properties, while most of the algorithms are still under rapid developments. One session of the proposed symposium will be dedicated to the developments and applications of theoretical methods for predicting phase transitions and the related properties of materials under pressure, motivating a discussion towards more efficient algorithms. One or two sessions of the proposed symposium will be dedicated to the experimental synthesis and characterizations of superconductors, topological insulators and two-dimensional materials under extreme strains. Invited speakers will deliver presentations from fundamental method developments to engineering applications, boosting the synergy between simulation and experiment for accelerated new materials discovery.