Structure is the most fundamental characteristics of a material. X-ray crystallography allows one to determine how atoms are arranged in a molecule and how molecules pack into a crystal. However, it requires a high-quality crystal sample, which is time consuming to prepare and often impossible under extreme conditions.

Theory has been playing a significant role in understanding crystal structures. Pauling summarized the rules for crystal structures of ionic solids,¹  however, similar powerful rules are still lacking for metals. First attempts to use computers to predict crystal structures date back to 1980. Although not very successful at the beginning,^2,3  crystal structure prediction (CSP) began to play an important role nowadays, thanks to many progresses in the last decade.^4–13  Indeed, mathematicians have developed algorithms to solve similar problems. Some of them are quite general and thus could be applied to crystal structure prediction. One can refer to a recent book¹⁴  for a discussion of different methods. In this chapter, we will briefly introduce the modern structure prediction techniques, and review the recent developments in the context of the USPEX method, which is based on the evolutionary algorithm (EA), and has been viewed as a revolution in crystallography.¹⁵  Discussions here follow closely the previous literature,^16–18  with primary focus on the most recent developments.