This work fills the gap for a comprehensive reference conveying the developments in global optimization of atomic structures using genetic algorithms. Over the last few decades, such algorithms based on mimicking the processes of natural evolution have made their way from computer science disciplines to solid states physics and chemistry, where they have demonstrated their versatility and predictive power for many materials. Following an introduction and historical perspective, the text moves on to provide an in-depth description of the algorithm before describing its applications to crystal structure prediction, atomic clusters, surface and interface reconstructions, and quasi one-dimensional nanostructures. The final chapters provide a brief account of other methods for atomic structure optimization and perspectives on the future of the field.