Relative to other temnospondyls, edopoids also have enlarged premaxillae, maxillae, and nasal bones in the snout region, which constrict the nostrils to small holes and push them to the sides of the skull.

The lack of sensory sulci suggests that most edopoids were adapted to terrestrial lifestyles, as lateral lines are characteristic of aquatic animals.

Edopoidea was named as a superfamily of temnospondyls by American paleontologist Alfred Romer in the second edition of his textbook Vertebrate Paleontology, published in 1945.

Below is a cladogram showing the relationships of edopoids from Sidor et al. (2006):[5] Balanerpeton woodi Capetus palustris Saharastega moradiensis Edops craigi Procochleosaurus jarrowensis Adamanterpeton ohioensis Cochleosaurus bohemicus Cochleosaurus florensis Nigerpeton ricqlesi Chenoprosopus milleri Chenoprosopus lewisi Eryops megacephalus and other derived temnospondyls Most edopoids are known from the Late Carboniferous and Early Permian of Europe and North America, which at the time formed a larger continent called Euramerica.

Tropical and subtropical environments were likely widespread across Euramerica during the Carboniferous and Early Permian, meaning that edopoids could easily travel between what are now North America and Europe.