Crystal structure prediction is an important first step on the path toward computational materials design. Increasingly robust methods have become available in recent years for computing many materials properties, but because properties are largely a function of crystal structure, the structure must be known before these methods can be brought to bear. In addition, structure prediction is particularly useful for identifying low-energy structures of subperiodic materials, such as two- dimensional (2D) materials, which may adopt unexpected structures that differ from those of the corresponding bulk phases. Evolutionary algorithms, which are heuristics for global optimization inspired by biological evolution, have proven to be a fruitful approach for tackling the problem of crystal structure prediction. This thesis describes the development of an improved evolutionary algorithm for structure prediction and several applications of the algorithm to predict the structures of novel low-energy 2D materials. The first part of this thesis contains an overview of evolutionary algorithms for crystal structure prediction and presents our implementation, including de- tails of extending the algorithm to search for clusters, wires, and 2D materials, improvements to efficiency when running in parallel, improved composition space sampling, and the ability to search for partial phase diagrams. We then present several applications of the evolutionary algorithm to 2D systems, including InP, the C-Si and Sn-S phase diagrams, and several group-IV dioxides. This thesis makes use of the Cornell graduate school’s “papers” option. Chap- ters 1 and 3 correspond to the first-author publications of Refs. [131] and [132], respectively, and chapter 2 will soon be submitted as a first-author publication. The material in chapter 4 is taken from Ref. [144], in which I share joint first- authorship. In this case I have included only my own contributions.