The Gloria is sung Mass on all Sundays outside of the seasons of Advent and Lent, as well as all solemnities and feasts. In the current Missal it is sung during the Introductory Rites, after the Penitential Act, and followed by the Collect prayer.
One of the first instructions that the Gloria should be sung at Mass comes from the Gregorian Sacramentary, a book from the seventh or eight century governing papal liturgies. However, the Gloria could only be sung at Masses with the Bishop, except during the Easter season. By the publication of the Roman Missal in 1570, the Gloria was sung often at Mass. The priest intoned the first line, "Gloria in excelsis Deo," and usually the choir took up the remainder. It could take a while, so the assembly often sat down until the choir was finished!
The 1970 Roman Missal actually reduced the number of occasions when the Gloria was sung, so that the Introductory Rites would be more festive on those days, but more focused when it was omitted.
The 2002 Roman Missal instructs that the Gloria is intoned by the priest, or if necessary, by the cantor or the choir. This tradition goes back many centuries when the Bishop, immediately following the Entrance Procession, would be the first to raise his voice in praise of God, even before greeting the people.
In the deliberations to revise the liturgy following the Second Vatican Council, the position of the Gloria was considered, even with the possibility of moving it closer to the end of Mass, after the Prayer after Communion. However, it retained its traditional place following the Kyrie.
And this is a polyphonic choral setting by Victoria, composed during the Renaissance... note the intonation of the "Gloria in excelsis Deo," to the same chant melody from the Mass XV version. Listen here: Gloria from Missa O Magnum Mysterium by Tomas Luis de Victoria