The layout of this thesis is as follows: In Chapter 2 we describe the methods employed in this thesis, the global optimization technique - standard evolutionary approach in crystal structure prediction and its possible extensions, as well as local structural optimization (potential functions and optimization algorithms). In Chapter 3, we introduce a new constrained evolutionary algorithm to predict the crystal structures for materials containing molecular units. Chapter 4 gives an example to illustrate the power of the constrained evolutionary algorithm by applying it to study one promising materials for hydrogen storage, Mg(BH). In Chapter 5 and 6, we report our results for the stoichiometric variations on two types of oxides, Xe-O and Mg-O systems under high pressures. In Chapter 7, we introduce a new function of structural search - to look for the structures with highest density for carbon. In Chapter 8, we propose a new CSP method which combines the features of both evolutionary algorithm and metadynamics method, and apply it to all low-enthalpy structures accessible from graphite.