Can symmetry be utilized as a design principle to constrain evolutionary search, making it more effective? This dissertation aims to show that this is indeed the case, in two ways. First, an approach called ENSO is developed to evolve modular neural network controllers for simulated multilegged robots. Inspired by how symmetric organisms have evolved in nature, ENSO utilizes group theory to break symmetry systematically, constraining evolution to explore promising regions of the search space. As a result, it evolves effective controllers even when the appropriate symmetry constraints are difficult to design by hand. The controllers perform equally well when transferred from simulation to a physical robot. Second, the same principle is used to evolve minimal-size sorting networks. In this different domain, a different instantiation of the same principle is effective: building the desired symmetry step-by-step. This approach is more scalable than previous methods and finds smaller networks, thereby demonstrating that the principle is general. Thus, evolutionary search that utilizes symmetry constraints is shown to be effective in a range of challenging applications.