Brachiopod orders

thumb|Hemithiris psittacea, a living rhynchonellide thumb|Ladogia sp., a rhynchonellid brachiopod from the Devonian of western [[Russia (side view).]]

Terebratulids are one of only three living orders of articulate brachiopods, the others being the Rhynchonellida and the Thecideida. Craniida and Lingulida include living brachiopods, but are inarticulates. The name, Terebratula, may be derived from the Latin "terebra", meaning "hole-borer". The perceived resemblance of terebratulid shells to ancient Roman oil lamps gave the brachiopods their common name "lamp shell".

Lingulida is an order of brachiopods.

Acrotretides (Acrotretida) are an extinct order of linguliform brachiopods in the class Lingulata. Acrotretida contains 8 families within the sole superfamily Acrotretoidea. They lived from the Lower Cambrian to the Middle Devonian, rapidly diversifying during the middle Cambrian. In the upper Cambrian, linguliforms reached the apex of their diversity: acrotretides and their relatives the lingulides together comprised nearly 70% of brachiopod genera at this time. Though acrotretides continued to diversify during the Ordovician, their proportional dominance declined, as rhynchonelliforms took o

Thecideida is an order of cryptic articulate brachiopods characterized by their small size and habit of cementing their ventral valves to hard substrates such as shells, rocks and carbonate hardgrounds. Thecideides first appeared in the Triassic and are common today. thumb|Thecidium mediterraneum, A. natural size: B. section through shell (magnified)

Atrypida is an extinct order of rhynchonelliform brachiopods. They first appeared in middle Ordovician and survived the Ordovician-Silurian extinction, becoming the dominant brachiopods of the Silurian alongside the order Pentamerida. They would survive into the Late Devonian before going extinct at the end of the Frasnian (Late Devonian).