The evolution of amphibians is a long and complex narrative stretching back over 330 million years. The most diverse group is the temnospondyls, which display a myriad of peculiar and novel morphologies that are not found among modern amphibians like frogs and salamanders.
Most of my research on Paleozoic temnospondyls (for my dissertation) is related to a Permo-Carboniferous group known as the dissorophoids. Several clades within this group are known to have evolved terrestrial lifestyles, a relatively rare ecology as amphibians were outcompeted in many environments due to climate change and the evolution of amniotes (reptiles, etc.). Accompanying this lifestyle is a diverse array of morphological innovations and adaptations.
For example, one group of dissorophoids, the dissorophids (confusing names for sure), evolved to have bony plates (osteoderms) along their entire backbone, probably to help stiffen the spine (important when walking on land). Another group, the trematopids, have greatly enlarged nostrils, the exact function of which remains unresolved. The last terrestrial group, the amphibamids, underwent miniaturization, a rare occurrence among temnospondyls that has led them to often be closely tied to the origins of modern amphibian groups.
Because of their inferred relationship to modern amphibians, studying the anatomy, evolutionary relationships, development, and inferred ecology of these terrestrial temnospondyls is important for understanding the context in which modern amphibians evolved and could offer important insights into what aspects of their paleobiology allowed them to persist when so many other temnospondyls perished.