Abstract: Diverse forces have shaped the genomes of individuals throughout the world. It is crucial to understand those historical processes to study the genetics of individuals alive today. Nowhere else is this more important than in the study of admixed populations. A majority of individuals across the Americas are admixed, having received ancestry from sub-Saharan Africans, Europeans, and Indigenous Americans. However, to this day, admixed populations remain understudied, particularly because harnessing all information from their genomes requires in-depth population genetic analysis. This is not typically part of standard practice in genome-wide association studies. In this work I focus on two important aspects of understanding the history of admixed populations of the Americas to identify important associations with medical traits not possible using standard genetic analysis techniques. This work consists of two primary parts: 1) I develop a framework for genome-wide admixture mapping meta-analysis from high density SNP genotyping data. I use it to identify a novel, heritable risk factor for asthma in over 7,000 Latinos at the SMAD2 locus that could not be discovered using standard genotype association techniques. I then demonstrate the downstream use of blood-based expression of SMAD2 as a biomarker for both risk of exacerbation and poor response to bronchodilators in people with asthma. 2) Along with collaborators I developed the first fine-scale genetic map of indigenous and admixed populations across the country of Mexico, to determine how fine-scale differentiation of indigenous populations impacts the local communities of mixed ancestry. Using novel extensions of Principal Component Analysis we identify striking geographic correlations with the indigenous component of ancestry in admixed individuals, and use this data to identify for the first time a clinically meaningful association between indigenous American origins and lung function.