Hagfish, of the class Myxini (also known as Hyperotreti) and order Myxiniformes , are eel-shaped, slime-producing marine fish (occasionally called slime eels). They are the only known living animals that have a skull but no vertebral column, although hagfish do have rudimentary vertebrae. Along with lampreys, hagfish are jawless; the two form the sister group to jawed vertebrates, and living hagfish remain similar to hagfish from around 300 million years ago.

The classification of hagfish was once the subject of debate: was the hagfish a type of vertebrate that through evolution had lost its vertebrae, most closely related to lampreys (the earlier view), or did the hagfish represent a stage preceding the evolution of the vertebral column, as is the case with lancelets (the alternative view)? Recent DNA evidence has supported the earlier view.

The original scheme groups hagfish and lampreys together as cyclostomes (or historically, Agnatha), as the oldest surviving class of vertebrates alongside gnathostomes (the now-ubiquitous jawed vertebrates). The alternative scheme proposed that jawed vertebrates are more closely related to lampreys than to hagfish (i.e., that vertebrates include lampreys but exclude hagfish), and introduced the category craniata to group vertebrates near hagfish.