[aculeus]

Lampreys are the most "primitive" of the vertebrates, meaning that they are the least changed from the first vertebrates.

I thought all vertebrates by definition had back bones. But ...

"These are pretty insubstantial animals," Coates said. "Lacking a boney skeleton, they rot down, leaving no hard parts, like a skull or ribs. So if a fossil site is discovered that yields impressions of the delicate remains of these animals, then this site needs to be explored thoroughly for other examples of exceptional preservation."

Explanation?

[Oberon]

It has a cartilage skeleton, like a shark. No bones.

[Lee N. Field]

I thought all vertebrates by definition had back bones. But ...

Chordates with a cartilaginous spine.

[lepton]

It's a chordate.

[Stultis]

I thought all vertebrates by definition had back bones.

No. Not necessarily bones. They all have a vertebral column, which is not necessarily (and isn't) bony in the most primitive vertebrates.

The largest subgroup within the vertebrates is the craniata, which are animals with a skull. The lamprey is the most primitive of the craniates, with the least developed (and cartiliginous rather than bony) vetrebral column. The only more primitive vertebrate is the hagfish, which (IIRC) is the only living vertebrate that is NOT also a member of craniata. It has cartiliginous plates in it's head, like the lamprey, but unlike the lamprey it lacks a true braincase.

Back to the vertebral column, here's a diagram and discussion I found at The Tree of Life:

Characteristics

The Vertebrata have all the characteristics of the Craniata but share, in addition, a number of unique characteristics which do not occur in hagfishes (Hyperotreti). These characteristics are:

• Metamerically arranged endoskeletal elements flanking the spinal cord. There are primitively two pairs of such elements in each metamere and on each side: the interdorsals and basidorsals. In the gnathostomes, there are two additional pairs ventrally to the notochord: the interventrals and basiventrals. These elements are called arcualia and can fuse to a notochordal calcification, the centrum. The ensemble of the arcualia + centrum is the vertebra, and the ensemble of the vertebrae is the vertebral column.

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  The vertebrates are characterized by a vertebral column; that is, a variable number of endoskeletal elements aligned along the notochord (green) and flanking the spinal cord (yellow). In lampreys (top), the vertebral elements are only the basidorsal (red) and the interdorsals (blue). In the gnathostomes, there are in addition ventral elements, the basiventrals (purple) and interventrals (orange), and the notochord may calcify into centra (pink). (After Janvier 1996).