Kisspeptin (KISS1) and its receptor (KISS1R) are important regulators of the reproductive function, along with gonadoliberin (GnRH), gonadotropins (luteinizing hormone (LH) and follicle-stimulating hormone (FSH)), and sex steroid hormones. Mutations of their genes alter sexual maturation. The p.P74S, p.H90D, and p.P110T missense mutations of KISS1 are associated with central precocious puberty (CPP); and the p.G35S, p.C53R, and p.F117L mutations, with delayed puberty and isolated hypogonadotropic hypogonadism (IHH). The p.P196H and p.R386P mutations of KISS1R are also associated with CPP. However, a greater number of KISS1R mutations are associated with IHH, as is the case with p.L102P, p.L148S, p.E232Q, p.R297L, p.Y313H, pX399R, and more complex mutations, such as the 155-bp deletion that removes the acceptor splice site of intron 4 and part of exon 5, a deletion of the GCA triplet in position-2 ...-4 of intron 2, and an ACCGGCT insertion in the same site. The heterozygous compound mutations p.C223R/p.R297L and p.R331X/X399R and the 1-bp insertion 1001_1002insC of KISS1R are similarly associated with IHH. Leptin-dependent activation of KISS1 in hypothalamic neurons was observed in mice and sheep, being especially evident after puberty. Leptin exerts a permissive effect in regulating fertility and facilitate the induction of puberty by hypothalamic KISS1 and GnRH and pituitary LH and FSH, which support the reproductive function during further life.