The oldest circumscriptional names of the taxon under consideration are Orchesopia Rafinesque, 1815 and Saltatoria Latreille, 1817. The recent Saltatoria are divided into two subordinate taxa whose circumscriptional names are Dolichocera Bey-Bienko, 1964 and Caelifera Ander, 1936 [= Metorthoptera Crampton, 1927 = Brachycera Bey-Bienko, 1964 (non Brachycera Zetterstedt, 1842)]. The name Ensifera Chopard, 1920, according to its original circumscription, belongs to the taxon which includes Tridactylidae; the name Caelifera Ander, 1936 originally belongs to the taxon which also includes Tridactylidae; therefore, these two circumscriptional names cannot be used in the same classification. Saltatoria belong to Tegminoptera Kluge, 2013, which belong to Rhipineoptera Kluge, 2012. Holophyly of Saltatoria is well proved by autapomorphies, the most conclusive of which are the stagnofemoral leaping specialization of the hind legs with the irreversibly reduced trochanter, and the inversed position of protoptera at the penultimolarval and ultimolarval stages. All the Saltatoria can be divided into an extinct plesiomorphon Permorchesopia taxon n. (characterized by primitively 5-segmented tarsi) and Neorchesopia taxon n. (characterized by partial or complete fusion of the 1st and 2nd tarsomeres). The structure and evolution of ovipositors are discussed. The term kinetapophyses is proposed as a common name for homologous abdominal appendages: the retractile vesicles on the pregenital segments of Triplura and Diplura and the 1st and 2nd ovipositor valves on abdominal segments VIII and IX of female Amyocerata. The portion of the sternum containing the muscles that extend to the kinetapophyses and styli can be referred to either as a styliger, a bistyliger, or a pair of unistyligers; the term “coxite” should be avoided since it implies doubtful homologization of these appendages. In the digging ovipositor of Caelifera, the shortened kinetapophyses IX are not vestiges but functionally important components. Examination of Ripipteryx gives insight into the origin of the peculiar lateral apodemes present in the ovipositors of the other representatives of Caelifera. Based on new hypotheses about character polarity in the ovipositor morphology and about evolution of stridulatory and hearing apparatuses, a new phylogenetic classification of Saltatoria is suggested, in which Dolichocera includes taxa with new circumscriptional names Stratensifera taxon n., Acoustopoda taxon n., Mesensifera taxon n., Striduloptera taxon n., Tettigensifera taxon n., and Gryllensifera taxon n., and Caelifera includes taxa with new circumscriptional names Vectocaelifera taxon n. and Acoustogastra taxon n.