This thesis summarizes our efforts to study the structure and properties of materials computationally. The adaptive genetic algorithm (AGA) developed by us to predict crystal/surface/interface structures is presented. Applications of AGA to a variety of systems, such as non-rare earth magnetic materials, ultra-hard transition metal borides and SrTiO3 grain boundaries, are discussed. We demonstrated by AGA the capability of solving crystal structures with more than 100 atoms per unit cell and rapidly accessing the structures and phase stabilities of different compositions in multicomponent systems. We also introduced a motif-network scheme to study the complex crystal structures in silicate cathodes. In addition, we explored different computational methods for atomistic simulations of materials behavior, such as Monte Carlo modeling of the alnico magnets.