  Prediction of stable crystal structures at given pressure-temperature
conditions, based only on the knowledge of the chemical composition, is a
central problem of condensed matter physics. This extremely challenging problem
is often termed "crystal structure prediction problem", and recently developed
evolutionary algorithm USPEX (Universal Structure Predictor: Evolutionary
Xtallography) made an important progress in solving it, enabling efficient and
reliable prediction of structures with up to ~40 atoms in the unit cell using
ab initio methods. Here we review this methodology, as well as recent progress
in analyzing energy landscape of solids (which also helps to analyze results of
USPEX runs). We show several recent applications - (1) prediction of new
high-pressure phases of CaCO3, (2) search for the structure of the polymeric
phase of CO2 ("phase V"), (3) high-pressure phases of oxygen, (4) exploration
of possible stable compounds in the Xe-C system at high pressures, (5) exotic
high-pressure phases of elements boron and sodium.
