The definition and scope of Ordovician genera of agnostid trilobites are discussed, and the generic affiliation of Ordovician species and well-illustrated material referred to in open nomenclature is assessed. Some 198 Ordovician species plus 25 species of uncertain latest Cambrian/earliest Ordovician age are enumerated, representing 24 genera and subgenera, of which Geragnostus (Novoagnostus) n.subg. and Lotagnostus (Semagnostus) n.subg. are new. Geragnostella is ranked as a subgenus of Geragnostus. The species of Arthrorhachis are tentatively divided among a tardus species group and an elspethi species group. Species of Dividuagnostus are divided among a sensu stricto group and an early species group. Pseudorhaptagnostus Lermontova, 1951 is restored as senior synonym of Neoagnostus Kobayashi, 1955. It is concluded that Ordovician agnostids were largely adapted to temperate and colder water habitats.