To explore the genetic architecture of human overgrowth syndromes and human growth control, we performed experimental and bioinformatic analyses of 710 individuals with overgrowth (height and/or head circumference ≥+2 SD) and intellectual disability (OGID). We identified a causal mutation in 1 of 14 genes in 50% (353/710). This includes HIST1H1E, encoding histone H1.4, which has not been associated with a developmental disorder previously. The pathogenic HIST1H1E mutations are predicted to result in a product that is less effective in neutralizing negatively charged linker DNA because it has a reduced net charge, and in DNA binding and protein-protein interactions because key residues are truncated. Functional network analyses demonstrated that epigenetic regulation is a prominent biological process dysregulated in individuals with OGID. Mutations in six epigenetic regulation genes—NSD1, EZH2, DNMT3A, CHD8, HIST1H1E, and EED—accounted for 44% of individuals (311/710). There was significant overlap between the 14 genes involved in OGID and 611 genes in regions identified in GWASs to be associated with height (p = 6.84 × 10−8), suggesting that a common variation impacting function of genes involved in OGID influences height at a population level. Increased cellular growth is a hallmark of cancer and there was striking overlap between the genes involved in OGID and 260 somatically mutated cancer driver genes (p = 1.75 × 10−14). However, the mutation spectra of genes involved in OGID and cancer differ, suggesting complex genotype-phenotype relationships. These data reveal insights into the genetic control of human growth and demonstrate that exome sequencing in OGID has a high diagnostic yield.