Melchizedek
Who Melchizedek is — Shem, an angel, a Christophany — and why his order matters.
Hebrews 7:1-10
1For this Melchizedek, king of Salem, priest of God Most High, who met Abraham returning from the slaughter of the kings and blessed him,
2to whom also Abraham divided a tenth part of all (being first, by interpretation, “king of righteousness”, and then also “king of Salem”, which means “king of peace”,
3without father, without mother, without genealogy, having neither beginning of days nor end of life, but made like the Son of God), remains a priest continually.
4Now consider how great this man was, to whom even Abraham, the patriarch, gave a tenth out of the best plunder.
5They indeed of the sons of Levi who receive the priest’s office have a commandment to take tithes of the people according to the law, that is, of their brothers, though these have come out of the body of Abraham,
6but he whose genealogy is not counted from them has accepted tithes from Abraham, and has blessed him who has the promises.
7But without any dispute the lesser is blessed by the greater.
8Here people who die receive tithes, but there one receives tithes of whom it is testified that he lives.
9We can say that through Abraham even Levi, who receives tithes, has paid tithes,
10for he was yet in the body of his father when Melchizedek met him.
Genesis 14:18-20
18Melchizedek king of Salem brought out bread and wine. He was priest of God Most High.
19He blessed him, and said, “Blessed be Abram of God Most High, possessor of heaven and earth.
20Blessed be God Most High, who has delivered your enemies into your hand.” Abram gave him a tenth of all.
What each tradition says
Rabbinic / Midrashic
Rashi offers a Midrashic explanation that Melchizedek is identical with Shem, son of Noah, citing Nedarim 32b. He presents this identification as the Midrashic reading of the passage.
Rashi (R. Shlomo Yitzhaki, 1040-1105), Rashi on Genesis 14:18 — Pentateuch with Rashi's commentary by M. Rosenbaum and A.M. Silbermann (1929-1934), Sefaria — On Genesis 14:18 (comment on 'And Melchizedek')
Patristic
Chrysostom states that Melchizedek did have parents and did die. Yet Scripture calls him without father, without mother, and having neither beginning of days nor end of life because these things are not expressed.
John Chrysostom (c. 347-407), Homilies on the Epistle to the Hebrews (Nicene and Post-Nicene Fathers, ser. 1, vol. 14) — Homily XII, on Hebrews 7:3
Catholic
John Tierney writes that Scripture’s silence about the facts of Melchisedech’s birth and death was part of the divine plan. It made Melchisedech prefigure more strikingly the mysteries of Christ’s generation and the eternity of His priesthood.
John Tierney, The Catholic Encyclopedia (1911), art. "Melchisedech" — On the silence of Scripture (Hebrews 7:3)
Orthodox
John of Damascus says the table pre-imaged the mystical table. He also says that priest was a type and image of Christ, the true high-priest.
John of Damascus (c. 676-749), An Exact Exposition of the Orthodox Faith (trans. S. D. F. Salmond), in Nicene and Post-Nicene Fathers, ser. 2, vol. 9 — Book IV, ch. 13 ('Concerning the holy and immaculate Mysteries')
Reformed / Protestant
Calvin says it is certain that he descended from parents, but the Apostle does not speak of him here in his private capacity. Rather, the Apostle sets him forth as a type of Christ and therefore allows himself to see nothing in him except what Scripture contains.
John Calvin (1509-1564), Commentary on Hebrews (CCEL text of the Calvin Translation Society edition) — On Hebrews 7:3
Evangelical
Wesley suggests that the Holy Ghost seems to have concealed who Melchisedec was, on purpose so he might be a more eminent type of Christ. The only thing we know, Wesley says, is that he was a priest and king of Salem, or Jerusalem.
John Wesley (1703-1791), John Wesley's Notes on the Bible — Notes on Hebrews 7:3