Most human diseases and agriculturally important traits are controlled by many genes that, individually, have a small effect on phenotypic characteristics. Mapping these genes through genome-wide association studies (GWAS) is extremely difficult. Genes that have been identified thus far only explain a proportion of genetic variance, even for common traits that have been well studied such as human height. This phenomenon is called the mystery of missing heritability. We have contributed to solving this mystery through statistical innovations that increase the statistical power of GWAS. For example, to enlarge the contrast of genetic-marker effect over error, we developed a technique to cluster individuals into groups. This optimized grouping reduces the error by averaging out the measurement error for individuals. We called this new method, the Compressed Mixed Linear Model (CMLM) (Zhang. et al., Nature Genetics, 2010). The CMLM improves both statistical power and computing efficiency (speed).