Genome-wide association studies have provided empirical evidence that common diseases have a polygenic architecture, but with differences in estimable genetic architecture parameters such as proportion of the genomic sites associated with trait variation (polygenicity), the proportion of variance explained by those common DNA variants (SNP-based heritability), and signatures of selection evident from the relationship between allele frequency and effect size. Comparisons of genetic parameters across traits highlight that psychiatric disorders and other brain-related traits are significantly more polygenic than most other common diseases. Key questions are to understand in which tissues, cell-types, and biological contexts risk variants have a functional impact. We review recent progress and consider the next generation of experimental data needed to understand the biological basis of polygenic disorders.