Hirschsprung’s disease is a congenital disorder that occurs in 1:5000 live births. It is characterised by an absence of enteric neurons along a variable region of the gastrointestinal tract. Hirschsprung’s disease is classified as a multigenic disorder, because the same phenotype is associated with mutations in multiple distinct genes. Furthermore, the genetics of Hirschsprung’s disease are highly complex and not strictly Mendelian. The phenotypic variability and incomplete penetrance observed in Hirschsprung’s disease also suggests the involvement of modifier genes. Here, we summarise the current knowledge of the genetics underlying Hirschsprung’s disease based on human and animal studies, focusing on the principal causative genes, their interactions, and the role of modifier genes.