O Come O Come Emmanuel is my absolute favourite advent carol, and anticipates the birth of Jesus. It comes from a medieval chant, of the Roman Catholic liturgy, Veni Immanuel. The music found in hymn and carol books today was adapted by Thomas Helmore, and the text translated from the Latin by John Mason Neale.
The Ukrainian Bell Carol, also known as Carol of the Bells, was based on an old Ukrainian folk song, Shchedryk, adapted by the Ukrainian composer Mykola Leontovych, in anticipation of a plentiful year, and would be sung in Ukrainian villages on New Years Eve. The English lyrics are entirely different, and were written by Peter Wilhousky, an American with a Czech background; the melody had reminded him of bells, and the Slavic legend that bells rand out at midnight on the evening Jesus was born, and so the tune is now also associated with Christmas.