Congenital hypothyroidism (CH) may be primary, due to a defect affecting the thyroid gland itself, or central, due to impaired thyroid-stimulating hormone (TSH)-mediated stimulation of the thyroid gland as a result of hypothalamic or pituitary pathology. Primary CH is the most common neonatal endocrine disorder, traditionally subdivided into thyroid dysgenesis (TD), referring to a spectrum of thyroid developmental abnormalities, and dyshormonogenesis, where a defective molecular pathway for thyroid hormonogenesis results in failure of hormone production by a structurally intact gland. Delayed treatment of neonatal hypothyroidism may result in profound neurodevelopmental delay; therefore, CH is screened for in developed countries to facilitate prompt diagnosis. Central congenital hypothyroidism (CCH) is a rarer entity which may occur in isolation, or (more frequently) in association with additional pituitary hormone deficits. CCH is most commonly defined biochemically by failure of appropriate TSH elevation despite subnormal thyroid hormone levels and will therefore evade diagnosis in primary, TSH-based CH-screening programmes. This review will discuss recent genetic aetiological advances in CH and summarize epidemiological data and clinical diagnostic challenges, focussing on primary CH and isolated CCH.