Modern microscopy techniques opened new perspectives to look at colloidal clusters. It is now possible to visualize the colloidal particles forming the cluster, which provides relevant experimental data that can be combined with detailed information resulting from structural optimization to understand phenomena at the mesoscale. From the theoretical view point, short-ranged Morse pair potentials have been successfully applied to model interactions between colloidal particles, while the development of efficient global optimization methods has allowed one to face the difficult task of searching for the geometry of the cluster that minimizes energy. In this work, we have carried out a thorough review concerning the global optimization methods proposed in the literature. The optimization of the title systems relies on the methods especially designed to deal with atomic clusters. Studies involving the global optimization of colloidal clusters were also surveyed.