An account is presented of the design and application of Genetic Algorithms for the geometry optimization (energy minimization) of clusters and nanoparticles, where the interactions between atoms, ions or molecules are described by a variety of potential energy functions (force fields). Adetailed description is presented of the Birmingham Cluster Genetic Algorithm Program, developed in our group, and two specific applications are highlighted: the use of a GAto optimize the geometry and atom distribution in mixed Cu-Au clusters; and the use of an energy predator in an attempt to identify the lowest six isomers of C₄₀.