Recent achievements in synchrotron instrumentations have greatly improved the quality of powder diffraction data obtained from a diamond anvil cell. With structural refinement techniques, many new structures of solid materials at high pressures have been discovered. In a number of solids, these structural changes also induce metallization and lead to the appearance of superconductivity upon compressing. On the theoretical side, typical approaches for predicting/determining unknown high-pressure crystal structures usually involve dynamical processes. We have tried another approach based on evolutionary algorithms proposed recently. This is an attempt to predict the most stable crystal structure and energetically favourable meta-stable structures without any approximation on initial structures. During evolutionary procedures, randomly generated structures evolve gradually into lower energy phases after a few generations. We have investigated the high-pressure structures of calcium and predicted two new stable structures that might explain the diffraction pattern of Ca-IV and Ca-V. Another example will be presented is the prediction of a metastable single-bonded phase of nitrogen. The search of a synthetic strategy for novel materials with high-Tc has been a continuing challenge. Recently there have been several new proposals relating superconductivity with some tailgate signatures for prospective candidate materials. Among these proposals are (i) the occurrence of low vibrational frequencies (ii) simultaneous occurrence of dynamical and electronic instabilities. Here we demonstrated successfully that these conditions can be satisfied in a high pressure phase of SnH4. We predicted this material would be superconducting with a Tc close to 80 K at 120 GPa. Some other high-pressure superconductors will be briefly reviewed. = * Work done in collaboration with John S. Tse