The question how genetic variation and personal health are linked is one of the compelling puzzles facing scientists today. The ultimate goal is to exploit human variability to find genetic causes for multi-factorial diseases such as cancer and coronary heart disease. Recent technology improvement enables the typing of millions of single nucleotide polymorphisms (SNPs) for a large number of individuals. Consequently, there is a great need for efficient and accurate computational tools for rigorous and powerful analysis of these data. In my talk I am going to concentrate on two computational problems, which are an essential step in studying the data obtained by this technology: Accurate and efficient significance testing with a correction for population stratification and estimating local ancestries in admixed populations.