• Caridea
• Stenopodidea
• Reptantia, divided into:

• Polychelida
• Achelata
• Glypheoidea
• Astacidea
• Thalassinidea
• Anomala
• Brachyura

Pleocyemata is a sub-order of decapod crustaceans, erected by Martin Burkenroad in 1963. Burkenroad's classification replaced the earlier sub-orders of Natantia and Reptantia with the monophyletic groups Dendrobranchiata (prawns) and Pleocyemata. Pleocyemata contains all the members of the Reptantia (which is still used, but at a lower rank), as well as the Stenopodidea (which contains the so-called "boxer shrimp" or "barber-pole shrimp"), and Caridea, which contains all the true shrimp.

These taxa are united by a number of features, the most important of which is that the eggs are incubated by the female, and remain stuck to the pleopods (swimming legs) until they are ready to hatch. It is this characteristic that gives the group its name.

Reference - BURKENROAD, M. D. (1963): The evolution of the Eucarida (Crustacea,Eumalacostraca), in relation to the fossil record. Tulane Studies in Geology, 2 (1): 1-17.