The mother of the Lord
'Mother of my Lord' and 'blessed among women' — Theotokos, veneration and intercession; set beside 'my mother and brothers' (Mark 3:31-35) and Luke 11:27-28.
Luke 1:39-45
39Mary arose in those days and went into the hill country with haste, into a city of Judah,
40and entered into the house of Zacharias and greeted Elizabeth.
41When Elizabeth heard Mary’s greeting, the baby leaped in her womb; and Elizabeth was filled with the Holy Spirit.
42She called out with a loud voice and said, “Blessed are you among women, and blessed is the fruit of your womb!
43Why am I so favored, that the mother of my Lord should come to me?
44For behold, when the voice of your greeting came into my ears, the baby leaped in my womb for joy!
45Blessed is she who believed, for there will be a fulfillment of the things which have been spoken to her from the Lord!”
What each tradition says
Rabbinic / Midrashic
The Jewish Encyclopedia describes the story of the virgin-birth as a legend. Such legends, it says, are common to almost all folk-heroes and indicate their superiority to the rest of their people.
Joseph Jacobs, Kaufmann Kohler, Richard Gottheil, Samuel Krauss, The Jewish Encyclopedia, vol. 7, s.v. 'Jesus of Nazareth' (New York: Funk & Wagnalls, 1901-1906) — Section 'Sources of Life' (on the Gospels and their supernatural element)
Patristic
Gregory of Nazianzus states that if anyone does not believe that Holy Mary is the Mother of God, that person is severed from the Godhead. He states this as the consequence of not believing that Holy Mary is the Mother of God.
Gregory of Nazianzus (c. 329-390), Select Letters, Letter 101, To Cledonius the Priest Against Apollinarius, in Nicene and Post-Nicene Fathers, ser. 2, vol. 7 (trans. Charles Gordon Browne and James Edward Swallow; New York: Christian Literature Publishing Co., 1893) — Letter CI, the dogmatic section (against Apollinarius, on the Theotokos)
Catholic
Thomas Aquinas reasons that God was conceived and born of the Virgin. Since a woman is called a man's mother because she conceived and gave birth to him, the Blessed Virgin is truly called the Mother of God.
Thomas Aquinas (1225-1274); trans. Fathers of the English Dominican Province, Summa Theologiae, Second and Revised Edition (New Advent) — III, q.35, a.4 ('Whether the Blessed Virgin should be called the Mother of God?'), reply
Orthodox
John of Damascus states that since the one born of her was true God, she who bore the true God incarnate is the true Mother of God. He holds that God was born of her, not implying that the divinity of the Word received from her the beginning of its being.
John of Damascus (c. 675-c. 749), An Exact Exposition of the Orthodox Faith, in Nicene and Post-Nicene Fathers, ser. 2, vol. 9 (trans. S. D. F. Salmond; Edinburgh: T&T Clark, 1898) — Book III, ch. 12 (That the holy Virgin is the Mother of God: an argument directed against the Nestorians)
Reformed / Protestant
Calvin says Mary’s first blessedness was not carrying Christ in her womb, but being born again by the Spirit to new life, which was greater. Yet she is justly called blessed, since God honored her as mother of his Only Begotten Son, through whom she was spiritually renewed; praising Christ’s blessing reminds us of this honor.
John Calvin (1509-1564), Commentary on a Harmony of the Evangelists, Matthew, Mark, and Luke, vol. 1 (trans. William Pringle; Edinburgh: Calvin Translation Society) — Commentary on Luke 1:39-45, on verse 42
Evangelical
Barnes says Jesus acknowledged that his mother was happy and that it was an honor to be his mother. But Jesus taught that the chief happiness and highest honor is obeying the word of God. Compared with this, all earthly distinctions and honors are nothing; man's greatest dignity is keeping God's commandments and being prepared for heaven.
Albert Barnes (1798-1870), Notes on the New Testament, Explanatory and Practical (enlarged ed. by Robert Frew; CCEL carries the Baker reprint) — Note on Luke 11:27-28 (the site's paired text)