We have essentially no mechanistic understanding of gene/intelligence interactions. Rather, we have cohorts of people tagged with traits (educational achievement, tested IQ, height, etc), all sequenced, and then we can run correlation surveys across all their genomes to identify correlations between alleles and traits. When you do that, you get 10-30% heritability numbers; the gap between that and the range for MZ/DZ twin studies (the 50-80% you often see) is "the missing heritability problem".