Person

Melchizedek

A mysterious priest-king who appears in Genesis 14 as "king of Salem" and "priest of God Most High." He blesses Abram and receives a tithe from him. He surfaces twice more in the canon. Psalm 110:4 names the Messiah a "priest forever according to the order of Melchizedek." Hebrews 5-7 develops the typology at length. It treats Melchizedek as a figure whose priesthood is greater than the later Levitical / Aaronic priesthood and whose office foreshadows Christ's eternal high-priestly ministry.

Biblical appearances

Genesis 14:18-20, Melchizedek meets Abram as he returns from defeating the kings. He brings out bread and wine, blesses Abram as "priest of God Most High," and Abram gives him a tenth of all.
Psalm 110:4, a Davidic / Messianic psalm: "You are a priest forever according to the order of Melchizedek." This is cited more often in the New Testament than any other Old Testament verse.
Hebrews 5:6, 5:10, 6:20, 7:1-17, the extended typological argument. Melchizedek's priesthood is not by ancestral lineage. He has no recorded beginning or end of days. He is therefore a fitting type of Christ's eternal priesthood. The Levites (descendants of Abraham) tithed through Abraham to Melchizedek, which shows Melchizedek's superiority.

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Theological significance

Christological type. Hebrews reads Melchizedek as a deliberate prefigurement of Christ's high-priestly office: eternal, royal, non-Levitical, and mediating a better covenant.
Argument from priesthood-change. A change of priesthood requires a change of law (Heb 7:11-12). Because Christ is enthroned as priest "according to the order of Melchizedek," the Levitical priesthood, and the legal system bound to it, is superseded. This is the argumentative spine of Are Christians Still Under the Law.
Royal-priestly union. Melchizedek combines kingship and priesthood in one office. This prefigures Christ as both King and Priest, something the Levitical line (held strictly separate from the Davidic kingly line) could not.
Independence from Sinai. Melchizedek's priesthood predates the Mosaic Law by centuries. That shows priestly mediation between God and humanity is not rooted in or limited to the Sinaitic covenant.

Interpretive options

Typological figure (mainstream Protestant, Catholic, and patristic): a real historical priest-king whose office and silence of genealogy make him an apt type of Christ.
Christophany / pre-incarnate appearance of the Son: a minority view (some patristics, some modern interpreters) that Melchizedek is the pre-incarnate Christ. Held in tension with Heb 7:3 ("made like the Son of God"), which seems to distinguish them.
Angelic / supernatural figure: extracanonical Second Temple traditions (for example, the 11Q13 Melchizedek scroll at Qumran) develop Melchizedek as a heavenly redeemer figure. Canonical Hebrews does not adopt this, but it is informative for backdrop.
Shem, son of Noah (rabbinic): Targum Pseudo-Jonathan on Gen 14 and b. Nedarim 32b identify Melchizedek with Shem, making him the ancestral holder of a priesthood passed to Abraham and eventually to Levi. The reading has a real basis: it supplies the otherwise unnamed priest with a genealogy inside the Genesis narrative, and it explains how a legitimate priest existed before Sinai.

The Shem identification, and what actually answers it

The identification matters apologetically because it bears on Hebrews 7. If Melchizedek is Shem, then his father, mother, genealogy, birth and death are all on record, and the description at Heb 7:3 loses its force; and his priesthood becomes the same line that runs to Levi rather than a distinct and higher one, which is the premise the argument of Hebrews 7 needs.

Two responses, in order of strength.

Chronology. On the longer chronology of Genesis 11 Chronology, preserved in the Septuagint and Samaritan Pentateuch, Shem dies roughly five centuries before Abraham is born, so he cannot be the priest who brings out bread and wine to Abraham in Gen 14. On the Masoretic figures the two lifetimes do overlap, which is why the identification is chronologically available in the first place. The argument therefore turns on a textual question, and should be presented that way rather than asserted flatly.
The text of Hebrews. Heb 7:3 says Melchizedek is "made like the Son of God," and the argument of Hebrews 7 turns on what the Genesis narrative records, not on metaphysics: Genesis gives this priest no lineage and no death notice, and Hebrews reasons from that silence. A named son of Noah with a recorded genealogy does not fit the way Genesis presents him, whatever the chronology.

Do not argue that the identification was invented to defeat Christian claims, or that the Masoretic genealogy was shortened deliberately to make it possible. The tradition is attested in its own right and has an internal rationale; the motive charge is an accusation the sources do not support, and this codex repudiates the Jews-altered-the-text trope wherever it appears. See The Jewish Defense and Genesis 11 Chronology.