Crystal structure determination is one of grand challenges in high-pressure materials science, and the structure prediction by computer simulations based on ab-initio calculations has played a significantly important role for it. In this article, metadynamics and genetic algorithm are focused on as the computational technique of the crystal structure searching. First, phosphorus and calcium are brought up as successful examples of the ab-initio metadynamics simulation. Then, the high-pressure phases of yttrium are shown as the results obtained by the application of the ab-initio genetic algorithm. In addition, for the three elements, the superconducting properties theoretically obtained by the use of the predicted crystal structures are compared with experimental ones.