Spectacular progress has been made in the characterization of human hyper-IgE syndrome (HIES) over the last 50 years. HIES is a primary immunodeficiency defined as an association of atopy in a context of very high serum IgE levels, characteristic bacterial and fungal diseases, low-level clinical and biological inflammation, and various non-hematopoietic developmental manifestations. Somewhat arbitrarily, three disorders were successively put forward as the underlying cause of HIES: autosomal dominant (AD) STAT3 deficiency, the only disorder corresponding to the original definition of HIES, and autosomal recessive (AR) DOCK8 and PGM3 deficiencies, in which atopy and high serum IgE levels occur in a context of manifestations not seen in patients with typical HIES. Indeed, these three disorders disrupt different molecular pathways, affect different cell types, and underlie different clinical phenotypes. Surprisingly, several other inherited inborn errors of immunity in which serum IgE levels are high, sometimes almost as high as those in HIES patients, are not considered to belong to the HIES group of diseases. Studies of HIES have been further complicated by the lack of a high serum IgE phenotype in all mouse models of the disease other than two Stat3 mutant strains. The study of infections in mutant mice has helped elucidate only some forms of HIES and infection. Mouse models of these conditions have also been used to study non-hematopoietic phenotypes for STAT3 deficiency, tissue-specific immunity for DOCK8 deficiency, and cell lineage maturation for PGM3 deficiency. We review here the history of the field of HIES since the first clinical description of this condition in 1966, together with the three disorders commonly referred to as HIES, focusing, in particular, on their mouse models. We propose the restriction of the term "HIES" to patients with an AD STAT3-deficiency phenotype, including the most recently described AR ZNF341 deficiency, thus excluding AR DOCK8 and PGM3 deficiencies from the definition of this disease.