The name Orthoptera refers to the straight veins of the forewings or elytra (or tegmina) and the orthopteroid orders form a group having incomplete metamorphosis, linked by the presence of three external characters: possession of unmodified mandibulate mouthparts, possession of cerci which are usually jointed and the presence of a large anal lobe in the hindwing. They also have two internal characters that link them - numerous Malpighian tubules and the presence of several separate ganglia in the ventral nerve-cord.
The Orthopteroid orders comprise the saltatorial or jumping group with enlarged, muscular hind legs, and the cursorial or walking group which include the older and more primitive orders. Other minor orders of hemimetabolous insects are associated with them within the Neoptera.
http://www.tolweb.org/Neoptera/8267
The Blattodea (cockroaches) are an extremely ancient group, appearing in the fossil records in the Carboniferous period over 300 million years ago and developing from the Protoblattodea, terrestrial predaceous insects with a concealed way of life as are the cockroaches with about 4,000 known species. Closely related to the cockroaches are the Mantodea (mantids) with about 2,500 species, the Grylloblattodea (ice-crawlers) with 20 species, the Isoptera (termites) with about 1,000 species, which have now been shown by DNA studies to be cockroaches which developed a particular mode of social organisation (http://www.nhm.ac.uk/about-us/news/2007/april/news_11364.html), the Dermaptera (earwigs) with about 1,000 species, the Phasmida (stick insects) with over 3,000 species and the recently described Mantophasmatodea (gladiators) with fifteen extant species.
http://www.mantophasmatodea.de/gladiator/index.htm
Ongoing DNA studies may further change current concepts.
http://www.treebase.org/treebase/console.html
http://www3.interscience.wiley.com/journal/119130681/abstract?CRETRY=1&SRETRY=0
There are two main groups (or suborders) of Saltatorial Orthoptera, the Ensifera and the Caelifera; there are fossil remains of the Ensifera from the Carboniferous, with the Caelifera developing through the Cretaceous and Triassic periods.
http://www.tolweb.org/Orthoptera
The Ensifera are named for the sword-shaped ovipositor (latin: ensis - a sword), and comprise theTettigonioidea (bush-crickets camel-crickets, king-crickets and wetas etc.) over 7,000 species and Grylloidea (true crickets and mole-crickets), about 2,000 species. They have very long, many-segmented, often thread-like antennae, their hearing organs (if present) are at the base of the fore-tibiae, and they sing by rubbing the forewings over each other; so a cricket which has had the misfortune to lose both hind legs may still produce a normal song. This group are widely omnivorous, some are predatory, often nocturnal.
The Caelifera are also named for the shape of the ovipositor, which is short and upcurved like an engraving tool (latin: caelum - engraving
tool), and comprise the Acridoidea (grasshoppers and locusts, groundhoppers, stick grasshoppers, monkey grasshoppers, etc.) with over 12,000 species and the Tridactyloidea (pygmy mole-crickets) with over 100 species. These insects have short, fairly stout antennae with a limited number of segments, their hearing organs are on side of the abdomen, and they usually sing by rubbing a row of stridulatory pegs on the inside of each hind femur against prominent veins on the flexed forewings. A grasshopper which has lost one hind leg may still sing, but the song may be slightly different from usual; if both hind legs are lost, so is their song! All are herbivorous and mainly diurnal.
The nomenclature and taxonomy of the Orthoptera is in a state of debate, and has been so for the last century, so that the number and level of family-group and even ordinal names may vary considerably according to which specialist is consulted.