The spiritual body
What the resurrection body is — material, transformed, or a body of another order.
1 Corinthians 15:35-49
35But someone will say, “How are the dead raised?” and, “With what kind of body do they come?”
36You foolish one, that which you yourself sow is not made alive unless it dies.
37That which you sow, you don’t sow the body that will be, but a bare grain, maybe of wheat, or of some other kind.
38But God gives it a body even as it pleased him, and to each seed a body of its own.
39All flesh is not the same flesh, but there is one flesh of men, another flesh of animals, another of fish, and another of birds.
40There are also celestial bodies and terrestrial bodies; but the glory of the celestial differs from that of the terrestrial.
41There is one glory of the sun, another glory of the moon, and another glory of the stars; for one star differs from another star in glory.
42So also is the resurrection of the dead. The body is sown perishable; it is raised imperishable.
43It is sown in dishonor; it is raised in glory. It is sown in weakness; it is raised in power.
44It is sown a natural body; it is raised a spiritual body. There is a natural body and there is also a spiritual body.
45So also it is written, “The first man, Adam, became a living soul.” The last Adam became a life-giving spirit.
46However that which is spiritual isn’t first, but that which is natural, then that which is spiritual.
47The first man is of the earth, made of dust. The second man is the Lord from heaven.
48As is the one made of dust, such are those who are also made of dust; and as is the heavenly, such are they also that are heavenly.
49As we have borne the image of those made of dust, let’s also bear the image of the heavenly.
What each tradition says
Rabbinic / Midrashic
According to the Jewish Encyclopedia, the Ethiopic Enoch apocalypse, composed a few years after Daniel, held that only righteous Israelites would experience a resurrection. That resurrection was to be bodily, and the body was to be subsequently transformed.
Executive Committee of the Editorial Board, Resurrection (The Jewish Encyclopedia, 1901-1906) — In Extra-Canonical Apocalypses (the resurrection body transformed)
Patristic
Chrysostom says that “a spiritual body” may mean either some such thing as was intimated by that phrase, or a body that is lighter and more subtle, even able to be wafted upon air. Or rather, he says, both meanings may be intended.
John Chrysostom, Homilies on the First Epistle to the Corinthians (NPNF ser. 1, vol. 12) — Homily XLI on 1 Cor. xv. 35-36 (on 'a spiritual body')
Catholic
Aquinas holds that the body will rise again identically the same, but in a different condition. It was mortal, and it will rise in immortality.
Thomas Aquinas, Summa Theologiae, Supplement (Second and Revised Edition, 1920) — Suppl. Q. 79, art. 1, Reply to Objection 1 (identity of the risen body)
Orthodox
Cyril of Jerusalem says all will be raised with eternal bodies, but not the same bodies. The righteous receive a heavenly body fit for converse with Angels; sinners receive an eternal body fit to endure sin's penalties, burning forever in fire without being consumed.
Cyril of Jerusalem, Catechetical Lectures (NPNF ser. 2, vol. 7) — Lecture XVIII, §19 (on the resurrection of the flesh: the heavenly body)
Reformed / Protestant
Calvin says the simple and genuine meaning of Paul is that the spiritual body does not mean the body’s substance will become spiritual. Paul does not mention substance here, and no change will be made upon it. No one should philosophize farther into airy speculations.
John Calvin, Commentary on the Epistles to the Corinthians, vol. 2 (Calvin Translation Society) — Comment on 1 Corinthians 15:44 (the 'spiritual body')
Evangelical
Wesley says the body is sown as merely animal, maintained by food, sleep, and air like the bodies of brutes. It is raised with a more refined contexture, needing none of these animal refreshments and endued with spiritual qualities, like the angels of God.
John Wesley, Wesley's Notes on the Bible, 1 Corinthians (Wesley Center Online) — Notes on 1 Corinthians 15:44