What is the Sub Tuum Praesidium?

It is an ancient prayer to the Blessed Virgin Mary, the oldest known version of which is found on an Egyptian papyrus from the 3rd century. This prayer is used in Litanies to the Blessed Mother and as a concluding prayer to Compline. 

The earliest text of this hymn was found in a Coptic Orthodox Christmas liturgy. The papyrus records the hymn in Greek, dated to the 3rd century by papyrologist E. Lobel and by scholar C.H. Roberts to the 4th century. According to scholar Serafim Seppälä, "there are no determinate theological or philological reasons to reject the 3rd-century dating."

It was part of the Sulpician custom that all classes ended with a recitation of this prayer. Besides the Greek text, ancient versions can be found in Coptic, Syriac, Armenian and Latin.

Henri de Villiers finds in the term "blessed" a reference to the salutation by Saint Elizabeth in Luke 1:42. 'Praesidium' is translated as "an assistance given in time of war by fresh troops in a strong manner."

The former medieval and post-medieval practice in several dioceses, especially in France, was to use the Sub tuum as the final antiphon at Compline instead of the Salve Regina, and in the Rite of Braga, where it is sung at the end of Mass.

A partial indulgence is granted to the faithful who recite it.

Latin:

Sub tuum praesidium confugimus, Sancta Dei Genetrix. Nostras deprecationes ne despicias in necessitatibus nostris, sed a periculis cunctis libera nos semper, Virgo gloriosa et benedicta. Amen.

Greek:

Ὑπὸ τὴν σὴν εὐσπλαγχνίαν,καταφεύγομεν, Θεοτόκε.Τὰς ἡμῶν ἱκεσίας,μὴ παρίδῃς ἐν περιστάσει,ἀλλ᾽ ἐκ κινδύνων λύτρωσαι ἡμᾶς,μόνη Ἁγνή, μόνη εὐλογημένη.

English:

We fly to thy patronage, O holy Mother of God; despise not our petitions in our necessities, but deliver us always from all dangers, O glorious and blessed Virgin. Amen.

And, an Eastern Version:

Beneath thy mercy, we take refuge, O Virgin Theotokos: disdain not our supplications in our distress, but deliver us from perils, O only Pure and Blessed One.