Congenital hypogonadotropic hypogonadism (CHH) and Kallmann syndrome (KS) are rare, related diseases that prevent normal pubertal development and cause infertility in affected men and women. However, the infertility carries a good prognosis as increasing numbers of patients with CHH/KS are now able to have children through medically assisted procreation. These are genetic diseases that can be transmitted to patients’ offspring. Importantly, patients and their families should be informed of this risk and given genetic counseling. CHH and KS are phenotypically and genetically heterogeneous diseases in which the risk of transmission largely depends on the gene(s) responsible(s). Inheritance may be classically Mendelian yet more complex; oligogenic modes of transmission have also been described. The prevalence of oligogenicity has risen dramatically since the advent of massively parallel next-generation sequencing (NGS) in which tens, hundreds or thousands of genes are sequenced at the same time. NGS is medically and economically more efficient and more rapid than traditional Sanger sequencing and is increasingly being used in medical practice. Thus, it seems plausible that oligogenic forms of CHH/KS will be increasingly identified making genetic counseling even more complex. In this context, the main challenge will be to differentiate true oligogenism from situations when several rare variants that do not have a clear phenotypic effect are identified by chance. This review aims to summarize the genetics of CHH/KS and to discuss the challenges of oligogenic transmission and also its role in incomplete penetrance and variable expressivity in a perspective of genetic counseling.