Zucchetto or Skull Cap
The scull cap worn by Catholic clergy is called the zucchetto (It.). It is similar in appearance, but not identical, to the yarmulke, which Jewish men are required to wear during any sacred ceremonies or in a sacred place. In his book on ecclesiastical protocol, The Church Visible, James-Charles Noonan devotes a chapter to it.
It original use was purely practical. Clerics were tonsured, had a ring of hair removed off the top of their head when they embraced celibacy. The skull-cap was meant to cover it and retain body heat, an absolute necessity in the unheated churches and monasteries of the past. From this practical use it acquired the role of identifying ecclesiastical rank by the color of the zucchetto.
Current use is governed by a Motu Proprio of Pope Paul VI in 1968, who made the zucchetto obligatory only for members of the hierarchy. Other clerics may use it. Previously, a seminarian became a cleric on the assumption of celibacy which occurred with sub-diaconate. Since that stage leading to Sacred Orders was abolished for the Latin-Rite, a man becomes a cleric with ordination to the diaconate.
White - Pope. This use developed in the 1500s. Previously the popes had their own distinctive cap, called a camauro. White became the papal color with the ascension of Pope Pius V, a Dominican, to the chair of Peter. He retained his Dominican habit. Religious orders whose habit is white, like the Dominicans and Norbertines, may also wear a white zucchetto.
Red - Cardinals. Pope Pius II decreed this color for cardinals in 1464.
Amaranth red - Patriarchs, Archbishops, Bishops. This violet color has only been the official episcopal color since 1867, when Pius IX replaced the black zucchetto of bishops, the color previously common to all clerics below the rank of Cardinal.
Black - lower clergy. All priests and deacons may wear the black zucchetto, though it has fallen out of use, except in some monasteries.
Noonan mentions that only Roman supply houses seem to know how to make zucchettos properly so that they hug the skull in the unique way proper to them. Other sources end up with a yarmulke-like cap (the Jewish cap), rather than the Roman zucchetto.
When the zucchetto is worn it is worn outdoors, indoors and, if a bishop, in the liturgy. Other clerics are supposed to leave them in the sacristy. Within the liturgy if the prelate is not celebrating it is removed briefly when reverencing the altar. It is removed at the Sanctus and restored before the Our Father, during which it is worn. Noonan notes that some prelates have started removing them during the Gospel and Our Father, but this is against long-standing custom and law. The zucchetto is removed in the presence of the exposed Blessed Sacrament, in procession of the Blessed Sacrament and during veneration of, or blessing with, a relic of the True Cross. They are also removed in the presence of the Holy Father, except during the liturgy, when it is worn as previously stated. However, it is briefly removed as a reverential acknowledgement when addressing the Holy Father or referring to him in a liturgical or other public discourse at which he is present.