Phylogenetics
The branching order of these animals is fairly well understood. The suborders Caelifera and Ensifera appear to be monophyletic and Rhaphidophoridae is a sister group of Tettigoniidae. Pyrgomorphidae are the most basal group of Caelifera. Myrmecophilidae appear to form a clade with Gryllotalpidae instead of with Gryllidae. Additional work may be needed to confirm this.
Among the four subfamilies of Tettigoniidae the relationships are (Phaneropterinae + (Conocephalinae + (Bradyporinae + Tettigoniinae))); among six acridid subfamilies the relationships are (Oedipodinae + (Acridinae + (Gomphocerinae + (Oxyinae + (Calliptaminae + Cyrtacanthacridinae))))).
Read more about this topic: Orthoptera