Congenital hypogonadotropic hypogonadism (CHH) is a rare disease characterized by delayed/absent puberty and infertility due to an inadequate secretion or action of gonadotrophin-releasing hormone (GnRH), with an otherwise structurally and functionally normal hypothalamic-pituitary-gonadal (HPG) axis. CHH is genetically heterogeneous but, due to the infertility of affected individuals, most frequently emerges in a sporadic form, though numerous familial cases have also been registered. In around 50-60% of cases, CHH is associated with a variety of non-reproductive abnormalities, most commonly anosmia/hyposmia, which defines Kallmann Syndrome (KS) by its presence. Broadly-speaking, genetic defects that directly impact on hypothalamic secretion, regulation, or action of GnRH result in a pure neuroendocrine phenotype, normosmic CHH (nCHH), whereas genetic defects that impact of embryonic migration of GnRH neurons to the hypothalamus most commonly result in KS, though nCHH can also arise. Hence, the description of several pedigrees, comprising subjects exhibiting KS and others with nCHH. Although more than 24 genes have been described to be involved in CHH, molecular variants of these do not presently explain more than 35-45% of reported cases. Therefore, numerous other unidentified genes (or conceivably, epigenetic mechanisms) remain to be described to fully understand the pathogenesis of CHH, explaining the emergent idea that CHH is a complex genetic disease characterized by variable expressivity and penetrance. This review summarizes the current state of knowledge on the complex genetic basis of congenital hypogonadotropic hypogonadism and aims to be accessible to both researchers and clinicians.