After 150 year study of trilobite fossils, there is still no overwhelming consensus. Some groups are put together as the suborder of an order and they could be put as separated order in some schemes. For example, Olenellida is put under Redlichiida (Prothero, 1998) while they are separated into different orders under Levi-Setti's classification. The major features used in classification include facial suture, number of segment, shape of pygidium and the structure of pleural lobes. There are 12-13 (sub)orders generally recognized.
The picture represents the evolution relationship
among the orders. Click the picture of the trilobite about which you like
to know more.
The picture is modified from Levi-Setti (1993).