The music was written by Manos Hadjidakis, with original Greek lyrics also by Manos Hadjidakis. The original Greek title is Τα Παιδιά του Πειραιά (Ta Paidiá tou Peiraiá) which translates as "The Children of Piraeus", and is the title commonly used in Greece. The original Greek lyrics do not make any mention of Sunday anywhere in the song.
The original Greek lyrics and also the foreign translations in German, French and Italian are true to the character of the Illya, the female main character of the movie. Illya is a jolly woman who loves life and the town and the people of her native Piraeus. And although she earns her money as a prostitute, she longs to find some day a man who is just as full of joie de vivre as Illya herself is.
The original version in Greek was recorded by Melina Mercouri, who also played the leading part of Illya in the movie. The song was a hit in the USA by Don Costa, whose orchestral version hit the charts in both 1960 and 1961, and the Chordettes, whose vocal cover just missed the top ten in 1961.
The song was used again in the 2005 movie Munich.
James Hill, a Canadian ukulele player, recorded a version of the song on ukulele for his album "A Flying Leap".