Congenital hypothyroidism (CH) is a state of insufficient thyroid hormone supply to the organism, starting in utero. Two forms of permanent primary or thyroidal CH are known. Thyroid dysgenesis (TD) describes a spectrum of defects of thyroid organogenesis. Five monogenetic forms due to mutations in TSHR, PAX8, NKX2-1, FOXE1 and NKX2-5 have been identified so far. Thyroid dyshormonogenesis comprises defects at every step of thyroid hormone synthesis. Mutations in 7 genes are well described causing iodine transport defect (SLC5A5), iodine organification defect (TPO, DUOX2, DUOXA2, SLC26A4), thyroglobulin (TG) synthesis or transport defect or iodotyrosine deiodinase (IYD/DEHAL1) deficiency. The new consensus guidelines for CH recommend genetic counseling for each family with an affected child. Mode of inheritance, recurrence rate and possible associated malformations in the context of syndromic forms should be outlined. Molecular genetic studies should be preceded by a detailed phenotypic description of the patient's thyroid disease and a detailed family history. This review summarizes clinical, biochemical and radiological phenotypes and molecular aspects of the known genetic forms of TD and thyroid dyshormonogenesis relevant for genetic counseling and molecular studies.