Down syndrome (DS) is the most common genetic cause of significant intellectual disability in the human population, occurring in roughly 1 in 700 live births. The ultimate cause of DS is trisomy of all or part of the set of genes located on chromosome 21. How this trisomy leads to the phenotype of DS is unclear. The completion of the DNA sequencing and annotation of the long arm of chromosome 21 was a critical step towards understanding the genetics of the phenotype. However, annotation of the chromosome continues and the functions of many genes on chromosome 21 remain uncertain. Recent findings about the structure of the human genome and of chromosome 21, in particular, and studies on mechanisms of gene regulation indicate that various genetic mechanisms may be contributors to the phenotype of DS and to the variability of the phenotype. These include variability of gene expression, the activity of transcription factors both encoded on chromosome 21 and encoded elsewhere in the genome, copy number polymorphisms, the function of conserved nongenic regions, microRNA activities, RNA editing, and perhaps DNA methylation. In this manuscript, we describe current knowledge about these genetic complexities and their likely importance in the context of DS. We identify gaps in current knowledge and suggest priorities to fill these gaps.