The biretta descends from the pileus, the soft round cap of the medieval universities, which was worn by graduates and which stiffened over time. Pressing a soft cap flat produces ridges, the ridges were then built in as raised peaks, and by the sixteenth century the shape was fixed: a stiff square cap with three or four upstanding blades and, usually, a tuft or pompon at the crown. The same ancestor, developing along a different line, produced the academic mortarboard, so a parish priest and a doctor of divinity in procession are wearing two descendants of one hat.
Colour marks rank rather than season. Black is worn by priests and deacons, purple by bishops, scarlet by cardinals, and white by some communities of canons regular. Three peaks are the ordinary form for clergy and a fourth is associated in some usages with doctorates. The tuft is omitted on a cardinal's biretta.
It is not a liturgical vestment in the sense that a chasuble is. It belongs to choir dress and to the ordinary outdoor and processional clothing of a cleric, and it goes over the cassock and surplice rather than over the vestments proper. Its Byzantine equivalents, the kalimavkion and the klobuk, are cylindrical and are worn by monastics as well as by clergy.