Holocephali (sometimes spelled Holocephala; Greek for "complete head" in reference to the fusion of upper jaw with the rest of the skull) is a subclass of cartilaginous fish. The only living holocephalans are three families which together are known commonly as chimaeras, but the group also includes many extinct members and was more diverse during the Paleozoic and Mesozoic eras. The earliest known fossils of holocephalans date to the Middle Devonian Epoch, and the subclass likely reached its peak diversity during the following Carboniferous Period. Molecular clock studies suggest that holocephalans diverged from their closest relatives, elasmobranchs such as sharks and rays, during the Early Devonian or the Silurian Period.

Extinct holocephalans are typically divided into a number of orders, although the interrelationships of these groups are poorly understood. Several different definitions of Holocephali exist, with the group sometimes considered a less inclusive clade within the larger subclasses Euchondrocephali or Subterbranchialia and with its members spread into the now obsolete groups Paraselachimorpha or Bradyodonti. Per these classification schemes, the name Holocephali is used only for chimaeras and their closest relatives. Recent research has suggested that the orders Cladoselachiformes and Symmoriiformes, which were historically considered relatives or ancestors of sharks, should instead be considered holocephalans. Information on the evolution and relationships of extinct holocephalans is limited, however, because most are known only from isolated teeth or dorsal fin spines, which form much of the basis of their classification.

Chimaeras, the only surviving holocephalans, include mostly deep-sea species which are found worldwide. They all possess broad, wing-like pectoral fins, a single soft cover over the gills, upper jaws which are fused to the skull, and six plate-like crushing teeth in the mouth. Males possess both two sets of paired sex organs around the pelvic fins and an unpaired, toothed structure termed a cephalic clasper on the head. Females reproduce by laying large, leathery egg cases. The skin of living chimaeras lacks scales or armor plates, with the exception of tooth-like scales termed dermal denticles on the sensory and sex organs. Chimaeras are unique among vertebrates in that their tooth plates contain organs called tritors, which are made of the mineral whitlockite. Fossils similar to living chimaeras are known as far back as the Early Carboniferous.

While some resembled their living relatives, many extinct holocephalans had skulls and bodies which were unlike modern chimaeras. In members of extinct groups, the upper jaws were often not fused to the rest of the skull and the jaws supported rows of separate, shark-like teeth. The bodies of most extinct holocephalans were totally covered in dermal denticles, which in Paleozoic and Mesozoic members were sometimes fused into armor plates. Many extinct holocephalans were sexually dimorphic, and the males of some species possessed large grasping organs on the head. In some groups the teeth were specialized into fused, curled structures termed "tooth whorls", or arranged into flattened, crushing surfaces termed "tooth pavements". The shape of the teeth in many extinct holocephalans suggests they had a diet of shelled prey, although other species instead likely hunted softer prey like cephalopods or smaller fish. Fossils of holocephalans are most abundant in shallow marine deposits, although an extinct species is known from freshwater environments as well.

The first published use of Holocephali (then spelled "Holocephala") was by naturalist Johannes Müller in 1835, and the group was formally defined and classified by naturalist Charles Lucien Bonaparte between 1832 and 1841. The name of the group comes from the Greek roots hólos meaning "whole" or "complete" and kephalos meaning head, and is in reference to the complete fusion of the braincase and the palatoquadrates (upper jaw) seen in chimaeras. As defined by Müller and Bonaparte, Holocephala encompassed the living genera Chimaera and Callorhinchus. Fossils of tooth plates and fin spines from the Mesozoic era were later assigned to Holocephali throughout the 1830s and 1840s. Many additional taxa were described and illustrated by the naturalist Louis Agassiz between 1833 and 1843, including a number of Paleozoic era tooth and spine genera now considered to belong to Holocephali. Both Agassiz and other influential researchers such as Richard Owen allied many Paleozoic representatives of the group with living Heterodontus (or Cestracion) sharks, rather than with chimaeras. By the late 1800s, researchers such as Fredrick McCoy and James William Davis questioned the relationship between these Paleozoic fossils and Heterodontus.

During the late 19th and early 20th century, British paleontologist Arthur Smith Woodward recognized many fossil chondrichthyans as forming a distinct taxonomic group, and in 1921 named this group Bradyodonti. Woodward considered Bradyodonti an order, although it was sometimes considered a class or subclass by later publications. He suggested that the bradyodonts were intermediate between sharks and chimaeras (then considered equivalent to Holocephali), and indicated that the latter had evolved from Paleozoic ancestors. Later work by the paleontologists Egil Nielsen and James Alan Moy-Thomas expanded the Bradyodonti to include the Eugeneodontiformes and Orodontiformes (then the families Edestidae and Orodontidae) as well as modern chimaeras, despite these taxa's differences from the group as defined by Woodward. The broadest usage of Bradyodonti is roughly equivalent to total-group Holocephali, and its composition remains similar to Holocephali as used by modern authors.

While treated as a subclass of the class Chondrichthyes by some authors (e.g. Joseph Nelson), Holocephali has alternatively been ranked as an order, a superorder, or a class. When Charles Lucien Bonaparte first defined Holocephala, he considered it to be an order within the larger subclass Elasmobranchii (different from modern usage; also contained the then-order selachii). Several authors during the 20th century regarded the Holocephali as its own class within the (now obsolete) superclass Elasmobranchiomorphi, which also included the classes Selachii (or Elasmobranchii), Arthrodira (or Placodermi), and under some definitions the Acanthodii. Holocephali is still sometimes considered a lower taxonomic unit within a larger subclass by some contemporary authors.

The interrelationships of extinct holocephalan orders have been characterized as difficult to define and subject to change, due in part to limited data. The orders Orodontiformes, Petalodontiformes, Iniopterygiformes, Debeeriiformes, Helodontiformes and Eugeneodontiformes were formerly united under the superorder Paraselachimorpha by researcher Richard Lund. The paraselachimorphs were defined as a sister group to either the superorder Holocephalimorpha (chimaeras and their closest relatives; also coined by Lund) or, in earlier works, the similarly defined Bradyodonti. However, Paraselachimorpha is now regarded as either paraphyletic or a non-diagnostic wastebasket taxon, including by Lund himself, and the taxa which formerly made up Paraselachimorpha are now considered an evolutionary grade of early-diverging holocephalans. Likewise, the historically significant order Bradyodonti, consisting variously of taxa now placed in Petalodontiformes, Orodontiformes, Eugeneodontiformes, Helodontiformes, Menaspiformes, Cochliodontiformes, Copodontiformes, Psammodontiformes, Chondrenchelyformes, and Chimaeriformes, has also been abandoned by recent authors and is considered a paraphyletic grade.