Understanding how genetic variation gives rise to phenotypic variation is a central goal of biology. The structure of this genotype-phenotype map, or landscape, underlies the dynamics of populations adapting under natural selection, and quantitative understanding will be required to predict and engineer outcomes in evolving organisms like viral pathogens, cancer cells, or microbial communities. Characterizing the landscape structure remains largely an empirical question, and observing general patterns requires high-throughput, high-powered experiments that systematically probe landscapes in different biological contexts. At the scale of a single protein, we considered the binding landscape of broadly neutralizing antibodies (bnAbs) that confer protection against diverse influenza strains. Our understanding of the evolutionary pathways leading to bnAbs, and thus how best to elicit them, remains limited. We measure binding affinities of combinatorially complete mutational libraries for two naturally isolated bnAbs, the first such libraries for antibodies and the largest for any protein (2 16 variants). By examining the extensive pairwise and higher-order epistasis between mutations, we find key sites with strong synergistic interactions that explain the strikingly different patterns of breadth in the two antibody libraries. These features of the binding affinity landscapes strongly favor sequential acquisition of affinity to more diverse antigens. At the whole-genome scale, we mapped the genetic basis of complex traits in budding yeast. Discrepancies exist between results from previous studies in humans as compared to model organisms, perhaps resulting from our limited ability to resolve numerous small-effect variants, precisely map them to causal genes, and infer nonadditive interactions between loci. We introduce barcoded bulk quantitative trait locus (BB-QTL) mapping, which allows us to construct, genotype, and phenotype 100,000 offspring of a budding yeast cross (100 times larger than state of the art). We find hundreds of small-effect loci densely spaced throughout the genome, many with widespread pleiotropic effects across multiple traits, consistent with results from recent genome-wide association studies in humans. Epistasis plays a central role, with thousands of interactions that reveal the structure of underlying biological networks.Ph.D.