In recent years population-based association studies have been advocated as the most powerful method of discovering genetic loci that are associated with heritable traits, particularly for complex traits that are likely caused by a variety of factors including environmental effects and multiple genetic loci. Genome-wide association studies (GWAS) have already yielded a large number of such associations, but there is growing concern that the results of these studies are not explaining as much genetic variation as they were expected to. Chapter 2 discusses tagging and imputation to leverage the information available on commercial genotyping chips to make inferences about variants found in large reference samples such as those made available by the International HapMap Consortium. Transferability of multi-marker tagging is assessed. Tagging and imputation are compared, and a method of using tagging to select a reduced tag set to be used for imputation. Chapter 3 details how multiple low frequency causal variants can create synthetic associations among more common variants and may be responsible for many of the genome-wide associations that have already been observed. Examples of synthetic associations are demonstrated in congenital deafness and sickle-cell anemia. Chapter 4 examines issues related to combining samples of diverse genetic ancestry for analysis in genetic association studies. Through simulation it is shown that type I error can be controlled and power increased using statistical methods to account for differences in populations.