Chordates form a phylum of creatures that are based on a bilateral body plan, and is defined by having at some stage in their lives all of the following: 1  A notochord, a fairly stiff rod of cartilage that extends along the inside of the body.t has also proved difficult to produce a detailed classification within the living chordates. Attempts to produce evolutionary  family trees  give results that differ from traditional classes because several of those classes are not monophyletic. As a result, vertebrate classification is in a state of flux.