Their heads had two sides; one, flat, was covered with large "pavement-like" plates, the other, convex, bore smaller plates. Their tails were long and segmented, resembling the stalk of a crinoid or the arm of a brittlestar. At the opposite end was a hole which may have been mouth or anus - or both.
They also bear features reminiscent of pharyngeal slits, a character lost in echinoderms but present in hemichordates.
Mitrates have been found with associated trace fossils. Their interpretation requires an understanding of how the animal was oriented in life; it's not agreed whether the convex side of the head was up or down, or indeed whether the "tail" was at the front or back of the organism! The trace fossils suggest that they pulled themselves through the mud with their "tail", and were flat-side up.