Since their first detection in 1996, highly pathogenic avian influenza viruses with H5 haemagglutinin of the A/Goose/Guangdong/1/1996 (Gs/Gd) lineage have caused outbreaks in domestic and wild animals associated with mass morbidity and mortality, and economic losses as well as sporadic human infections. These viruses have spread to hosts across the European, Asian, African, and North and South American continents, and most recently Antarctica, representing a major threat to wildlife, domestic animals and humans. Owing to continuous circulation in poultry, Gs/Gd lineage viruses have diversified into numerous distinct genetic and antigenic (sub)clades, and genetic diversity has further increased by extensive reassortment with low pathogenic avian influenza viruses of wild birds. In this Review, we discuss the historical emergence of Gs/Gd lineage viruses and their evolution and geographical spread. An overview of the major determinants of host range and cross-species transmission is provided to summarize phenotypic changes that may signal increased zoonotic or pandemic risks. The recent unusual outbreaks in wild carnivorous mammals and dairy cows is discussed, as well as the changing risk to humans. Countermeasures and mitigation strategies are described from the One Health perspective for future (pre-)pandemic preparedness.