Unlike many early Cambrian forms whose relationships are puzzling or worse, Aysheaia is remarkably similar to an obscure modern phylum the Onychophora. The modern forms include about 60 genera somewhat resembling both the Annelids and the Arthropods. The principal differences are that the Onychophora are terrestrial and have jaws whereas Aysheaia was marine and jawless. The Onychophora are soft bodied and have no structures such as teeth that would be expected to fossilize well. They have no fossil record except possibly three very ancient forms Aysheaia. Xenusion, and just possibly Hallucigenia.
A illustration of Aysheaia is available at: http://www.hrw.com/science/si-science/biology/animals/burgess/payshia.html