The gathering of the saints
'Caught up together with them in the clouds' (with Matthew 24:36-44) — a secret removal before the tribulation (the two-stage scheme of the nineteenth century), or a single return at the end (the post-tribulational and amillennial readings).
1 Thessalonians 4:13-18
13But we don’t want you to be ignorant, brothers, concerning those who have fallen asleep, so that you don’t grieve like the rest, who have no hope.
14For if we believe that Jesus died and rose again, even so God will bring with him those who have fallen asleep in Jesus.
15For this we tell you by the word of the Lord, that we who are alive, who are left until the coming of the Lord, will in no way precede those who have fallen asleep.
16For the Lord himself will descend from heaven with a shout, with the voice of the archangel and with God’s trumpet. The dead in Christ will rise first,
17then we who are alive, who are left, will be caught up together with them in the clouds, to meet the Lord in the air. So we will be with the Lord forever.
18Therefore comfort one another with these words.
What each tradition says
Rabbinic / Midrashic
Kaufmann Kohler states that the great trumpet blown to gather the tribes of Israel (Isa. xxvii. 13) will also rouse the dead. He cites Ber. 15b, Targ. Yer. to Ex. xx. 15, II Esd. iv. 23 et seq., I Cor. xv. 52, and I Thess. iv. 16.
Kaufmann Kohler, in Isidore Singer (ed.), The Jewish Encyclopedia, s.v. 'Eschatology' (New York: Funk & Wagnalls, 1901-1906) — Eschatology, section 'Resurrection of the Dead'
Patristic
Augustine reads “And so shall we ever be with the Lord” as not meaning we will always remain in the air with the Lord. Christ will not remain there but passes through as He comes. We meet Him as He comes, not where He remains, and are with Him in immortal bodies wherever we are with Him.
Catholic
Walter Drum states that Catholics insist Paul cannot have said the Parousia would occur during his lifetime. If Paul had said this, he would have erred, and the inspired word of God would err—the error being more of the Holy Spirit than of Paul.
Walter Drum, The Catholic Encyclopedia, vol. 14, s.v. 'Epistles to the Thessalonians' (New York: Robert Appleton Company, 1912) — Article, section 'Eschatology of Paul' (on 1 Thess. 4:15-17)
Orthodox
Chrysostom says Christ is about to descend, and we are caught up to meet him for honor. He compares this to a king entering a city: the honored go out to meet him, while the condemned wait within for the judge.
John Chrysostom (c. 347-407), Homilies on First Thessalonians (trans. James Tweed), in Nicene and Post-Nicene Fathers, ser. 1, vol. 13 (New York: Christian Literature Publishing Co., 1889) — Homily VIII, on 1 Thessalonians 4:15-17
Reformed / Protestant
Calvin says believers, once gathered into one kingdom, will have a life with no end, just as Christ’s life has no end. He rejects assigning Christ a thousand years and then having Him cease to reign, calling that too horrible even to mention.
John Calvin (1509-1564), Commentaries on the Epistles of Paul the Apostle to the Philippians, Colossians, and Thessalonians (trans. John Pringle, Calvin Translation Society, 1851) — Commentary on 1 Thessalonians 4:15-18, on verse 17
Evangelical
Albert Barnes states that the word’s proper meaning denotes a succession so close that it excludes any long interval in which other important transactions would occur. He gives a long personal reign of the Redeemer on earth as an example of such an interval.
Albert Barnes (1798-1870), Notes, Explanatory and Practical, on the New Testament: Thessalonians (New York: Harper & Brothers) — Notes on 1 Thessalonians 4:17
Evangelical
Darby states that the apostle clears up this point by distinguishing between the coming of Christ to take up His own and His day. He identifies His day as a day of judgment to the world.
John Nelson Darby (1800-1882), Synopsis of the Books of the Bible (London: G. Morrish, 1860; complete-scan 'Hodgett' edition) — On 1 Thessalonians 4 (the coming and the day)