Book excerpt: A central goal of evolutionary biology is to understand the nature and extent of genetic patterns underlying adaptive phenotypes. For example, when faced with similar environmental challenges, does evolution use similar molecular solutions, and if so, how are they similar? And do diverse changes in common traits arise from modifying different genes, or particular genes in different ways? The threespine stickleback provides an excellent model system to study these questions due to its unique natural history and diverse ecological niches. In my thesis work, I utilize experimental and computational approaches to both the parallel and divergent aspects of stickleback evolution to address these key evolutionary issues from multiple perspectives. To examine recurrent patterns in parallel evolution, I identify a large set of genomic loci that change repeatedly during colonization of new freshwater habitats by marine stickleback. The same loci used in these extant populations also show rapid allele frequency changes when new freshwater populations are experimentally established from marine ancestors. Both the speed and location of changes can be predicted using empirical observations of recurrence in natural populations or fundamental genomic features like allelic age, recombination rates, density of divergent loci, and overlap with mapped traits. A composite model trained on these stickleback features can also predict the location of key evolutionary loci in Darwin's finches and cichlids, suggesting similar features are important for evolution across diverse taxa. To study patterns in divergent evolution, I analyze different wild populations of freshwater stickleback that have either increased or decreased the lengths of their prominent dorsal and pelvic spines and identify a new regulatory locus with a major morphological effect on spine length. Natural alleles at this locus are differentiated between marine and freshwater sticklebacks; however, alleles found among freshwater populations are also differentiated, with distinct alleles found in short- and long-spined freshwater populations with reciprocal regulatory effects on the bone growth inhibitor gene Stanniocalcin2a. Many other stickleback loci similarly show three or more major alleles, suggesting that diverse alleles at key loci may represent a common mechanism for producing diverse phenotypes from a smaller toolkit of genes.