Nesidioblastoma and nesidioblastosis were terms given to neoplastic and non-neoplastic lesions of the pancreas associated with pancreatogenous hyperinsulinaemic hypoglycaemia. While nesidioblastoma was rapidly replaced by islet cell tumour, nesidioblastosis, defined as the proliferation of islet cells budding off from pancreatic ducts, was the diagnostic term associated with congenital hyperinsulinism of infancy (CHI) and adult non-neoplastic hyperinsulinaemic hypoglycaemia (ANHH). When it was shown that nesidioblastosis was not specific for CHI or ANHH, it was no longer applied to CHI but kept for the morphological diagnosis of ANHH. In severe CHI cases, a diffuse form with hypertrophic ß-cells in all islets can be distinguished from a focal form with hyperactive ß-cells changes in a limited adenomatoid hyperplastic area. Genetically, mutations were identified in several ß-cell genes involved in insulin secretion. Most common are mutations in the ABCC8 or KCNJ11 genes, solely affected in the diffuse form and associated with a focal maternal allelic loss on 11p15.5 in the focal form. Focal CHI can be localized by 18F-DOPA-PET and is thus curable by targeted resection. Diffuse CHI that fails medical treatment requires subtotal pancreatectomy. In ANHH, an idiopathic form can be distinguished from a form associated with gastric bypass, in whom GLP1-induced stimulation of the ß-cells is discussed. While the ß-cells in idiopathic ANHH are diffusely affected and are either hypertrophic or show only little changes, it is controversial whether there is a ß-cell increase or ß-cell hyperactivity in patients with gastric bypass. Recognizing morphological signs of ß-cell hyperactivity needs a good knowledge of the non-neoplastic endocrine pancreas across all ages.