Richard Hennig University of Florida Energy landscapes of materials control the materials' structure and thermodynamics, and kinetics. In this talk, I will start with a review of the essential physical, chemical, and geometric features and characteristics of energy landscapes that provide the foundation of optimization methods for structure searches. Next, I will present two complementary approaches to the exploration of energy landscapes: (i) data mining and (ii) evolutionary algorithms. Applications of these methods to the search for novel two-dimensional (2D) materials illustrates their usefulness and their limitations. The data mining of bulk materials databases using the scaling of the topology of the bonding network provides a useful algorithm to identify the dimensionality of structural motifs and results in over 600 low-energy 2D materials, which we make freely available in our 2D materials database at https://materialsweb.org. This approach requires the knowledge of layered bulk materials. Evolutionary algorithms enable an alternative approach to structure searches that does not rely on prior knowledge of materials. We have developed a grand-canonical genetic algorithm for structure prediction, GASP, to search for two-dimensional materials. The algorithm is available at https://github.com/henniggroup. Coupled with accurate quantum mechanical first-principles methods, we show that the evolutionary algorithm can successfully identify known structures of 2D materials, such as graphene and SnS2, explore the energy landscape of the 2D semiconductor InP, and discover several novel low-energy structures for 2D oxides.