Due to the complexity of high-dimensional potential energy surface, determining the ground state structure of a cluster is challenging. In recent years, there has been significant progress in the development of ab initio global optimization methods, such as genetic algorithm, basin hopping, topological methods, particle swarm optimization, tabu search, and minima hopping. The essential idea is to avoid being trapped in local minimum and to explore the entire region of potential energy surface. All these methods show remarkable performance in finding the ground state structures of various kinds of clusters. In this chapter, we present an overview of these methods.