The initiation and maintenance of reproductive capacity in humans is dependent on pulsatile secretion of the hypothalamic hormone GnRH. Congenital hypogonadotropic hypogonadism (CHH) is a rare disorder that results from the failure of the normal episodic GnRH secretion, leading to delayed puberty and infertility. CHH can be associated with an absent sense of smell, also termed Kallmann syndrome, or with other anomalies. CHH is characterized by rich genetic heterogeneity, with mutations in >30 genes identified to date acting either alone or in combination. CHH can be challenging to diagnose, particularly in early adolescence where the clinical picture mirrors that of constitutional delay of growth and puberty. Timely diagnosis and treatment will induce puberty, leading to improved sexual, bone, metabolic, and psychological health. In most cases, patients require lifelong treatment, yet a notable portion of male patients (∼10% to 20%) exhibit a spontaneous recovery of their reproductive function. Finally, fertility can be induced with pulsatile GnRH treatment or gonadotropin regimens in most patients. In summary, this review is a comprehensive synthesis of the current literature available regarding the diagnosis, patient management, and genetic foundations of CHH relative to normal reproductive development.