When two or more populations have been separated by geographic or cultural boundaries for many generations, drift, spontaneous mutations, differential selection pressures and other factors may lead to allele frequency differences among populations. If these ‘parental’ populations subsequently come together and begin inter-mating, disequilibrium among linked markers may span a greater genetic distance than it typically does among populations under panmixia [see glossary]. This extended disequilibrium can make association studies highly effective and more economical than disequilibrium mapping in panmictic populations since less marker loci are needed to detect regions of the genome that harbor phenotype-influencing loci. However, under some circumstances, this process of intermating (as well as other processes) can produce disequilibrium between pairs of unlinked loci and thus create the possibility of confounding or spurious associations due to this population stratification. Accordingly, researchers are advised to employ valid statistical tests for linkage disequilibrium mapping allowing conduct of genetic association studies that control for such confounding. Many recent papers have addressed this need. We provide a comprehensive review of advances made in recent years in correcting for population stratification and then evaluate and synthesize these methods based on statistical principles such as (1) randomization, (2) conditioning on sufficient statistics, and (3) identifying whether the method is based on testing the genotype-phenotype covariance (conditional upon familial information) and/or testing departures of the marginal distribution from the expected genotypic frequencies.