Chondrichthyes are monophyletic:

• cartilaginous endoskeleton calcified in a radial pattern.
• dermal skeleton represented by denticles of enameloid, dentine and basal tissue (dentine or bone).
• pelvic claspers.
• labial cartilages.
• triangular basal cartilage behind single dorsal fin spine.
• ceratotrichia in paired and unpaired fins.
• rectal gland (living forms).

There are two major (sister) groups within the Elasmobranchiomorpha (Chondrichthyes), the Holocephali and Elasmobranchii. In-group phylogeny remains uncertain, and under debate. The commonly recognized families are probably actually paraphyletic.

• autostylic jaws (palatoquadrate attached directly to the neurocranium).
• branchial arches under neurocranium.
• single gill cover.
• occipital collar or synarcual supporting base of neurocranium, typically of fused cervical vertebrae.

Superorder Squalomorph sharks. (Gill openings above pectoral fins).

Order Hexacanthoids (sixgills and sevengills or cowsharks and the frilled shark.)

Order Squaloids (spiny dogfish, bramble and sleeper sharks.)

Order Pristiophorids (sawsharks.)

Superorder Galeomorph sharks.

Order Heterodontoids (bullhead and horn sharks).

Order Orectoloboids (carpet, blind, nurse, zebra, whale, and wobbegong.)

Order Lamnoids (sand, tiger, crocodile, goblin, thresher, basking, mackeral, porbeagle, mako, and great white sharks.)

Order Characharinoids - dominant group (cat, false cat, hound, leopard, soupfin, tiger, gray, sharpnose, blue, lemon, and hammerhead.)

Superorder Squatinomorph "sharks" (angel shark).

Superorder Batoids. (Gill openings below pectoral fins).

Order Rhinobatoids (guitarfish.)

Order Rajiformes (skates.)

Suborder or family Rhinobatidae

Suborder or family Rajidae

Order Pristoids (sawfishes.)

Order Torpedinoids (torpedo or electric rays.)

Order Mylobatoids (stingrays, butterfly, eagle, cownosed, and devil rays.) - electric rays were used in electric shock therapy for some mentally ill in ancient Egypt.

Very successful, mainly are large predators eating large invertebrates and vertebrates. Chondrichthyans have solved the problems of living in water in different ways than later osteichthyan fishes. Differences affect all aspects of form and function:

Chondrichthyes have a cartilaginous skeleton, often strengthened with calcification. Cartilage is weak in bending, a property that permits reasonable locomotor performance in water only because fish do not have to support their body weight. Complete "skeleton" includes: the notochord, vertebral column, pectoral and pelvic girdles, and all tension transmitting, and compression resisting structures. Notochord constructed by centra built from cartilage or bone. The properties of cartilage and bone affect locomotion. Paired fins are supported by the pectoral and pelvic girdles. Chondrichthyan paired fins, like median fins, typically have numerous basal elements supported on a few endoskeletal elements extending beyond the body margin into the fin itself.

Elasmobranch kinematics are mainly undulatory, using the expanded pectoral fins in the batoidimorphs and the body/caudal fin in selachians. Oscillatory motions have evolved as derived characters in some clades. There is also a trend among more benthic selachians towards enhanced caudal area, especially expansion of the second dorsal fin.

Fish use hydrodynamic lift and hydrostatic lift from lipid inclusions to control posture and position in the water column. Dynamic lift originates with the anterior body and pectoral fins. Powered lift from the caudal fin, due to heterocercal organization and/or torsion and bending of the caudal peduncle.

Elasmobranchs have fused hemibranchs and a spiracle

A relatively thick skin has embedded placoid scales providing a light, flexible protective covering of small overlapping scales.

Teeth are modified placoid scales, which like the scales can be continuously shed and replaced. Teeth patterns vary with diet. Jaw suspension is also variable and affects ability to protrude jaws and suck substratum: autostylic, amphistylic, holostylic.

No unique senses, but in general: well developed olfactory system, vision, and electroreceptors.

Blood is hyper-osmotic (more concentrated) to seawater as a result of the retention of urea and tri-methylamine oxide (TMAO). Rectal gland used to excrete monovalent ions.

Telolecithal eggs are the rule, contained in thick cases - mermaids purses. Viviparity is common.