The name of the author of this psalm is unknown. There is no certain evidence that it was composed by David, yet there is nothing in the psalm itself which is inconsistent with the supposition that he was the author. Perhaps the most natural and obvious interpretation of Psalm 66:13-15, would be that there is reference there to the temple; and if so, of course, the psalm must have been written by someone else. But it is not absolutely necessary to suppose that the temple is there referred to, for the language might be applied to the tabernacle as the "house" or the place of the worship of God. There is, however, no positive evidence that it was composed by David, and it is impossible now to determine its authorship.
As little can the occasion on which the psalm was composed be determined. It is evident only that it was after there had been some calamity of a private nature, or after the nation had been subjected to oppression by some powerful enemies, and when there had been deliverance from that calamity, Psalm 66:11-12. The calamity was similar to those which had been endured by the nation in the time of the Egyptian oppressions, and naturally brought to mind the sufferings endured by the people of God at that time, while their own deliverance suggested a recollection of the deliverance of their fathers from that bondage, Psalm 66:6. On the whole, the supposition of Rosenmuller that it was composed after the Babylonian captivity, and in view of the return of the people to their native land - perhaps to be sung on their journey from the land of exile, seems to me to be the most probable of any. Venema supposes that it refers to the time of Hezekiah, and the overthrow of Sennacherib; others regard it as referring to the persecutions of David by Saul; others, to the rebellion of Absalom; others, to the famine which is mentioned in 2 Sam. 21, or the pestilence, 2 Sam. 24. Paulus supposes that it had reference to the times of the Maccabees. The psalm relates to "vows" or promises which had been made in a time of trouble; and its composition and use are designed as the fulfillment of those vows, Psalm 66:13-15. Such a psalm of praise would be a proper fulfillment of "vows" which it might be supposed the Hebrews would make in the time of their exile; to wit, that if they were ever permitted to return to their native land, they would go to the house of God, and sacrifice again on his altars.
On the phrase in the title, "To the chief Musician," see Introduction to Psalm 4:1-8. On the words, "A Song or Psalm," see the notes at the titles to Psalm 30:1-12 (notes) and Psalm 65:1-13 (notes).
The psalm contains:
I. An exhortation, addressed to all the earth, to praise God, as a matter pertaining to all lands, Psalm 66:1-2.
II. A reference to the mighty acts of God, as a reason for worshipping him, Psalm 66:3-7.
III. A reference to his gracious interposition in time of national danger and trouble, and to the fact that he had rescued the nation in a marvelous manner, Psalm 66:8-12.
IV. A reference to the vows which had been made in that time of trouble, and the purpose now to execute those vows, by going to the house of God, and sacrificing on his altars, Psalm 66:13-15.
V. A call on all people to hear what God had done for the worshippers: namely, That he had heard prayer; that he had interposed for their deliverance; that he had attended to the voice of supplication; that he had not turned away his mercy, Psalm 66:16-20.

The psalmist exhorts all to praise God for the wonders he has wrought, Psalm 66:1-4; calls on Israel to consider his mighty acts in behalf of their fathers, Psalm 66:5-7; his goodness in their own behalf Psalm 66:8-12; he resolves to pay his vows to God, and offer his promised sacrifices, Psalm 66:13-15; calls on all to hear what God had done for his soul, Psalm 66:15-20.
There is nothing particular in the title of the Psalm. It is not attributed to David either by the Hebrew, Chaldee, Syriac, Septuagint, Vulgate, or Ethiopic. The Arabic alone prefixes the name of David. The Vulgate, Septuagint, Ethiopic, and Arabic, call it a psalm of the resurrection: but for this there is no authority. By many of the ancients it is supposed to be a celebration of the restoration from the Babylonish captivity. Others think it commemorates the deliverance of Israel from Egypt, their introduction into the Promised Land, and the establishment of the worship of God in Jerusalem.

INTRODUCTION TO PSALM 66
To the chief Musician, A Song or Psalm. This psalm does not bear the name of David in the title of it, yet is generally thought to be one of his; but because the plural number is used in it, which is not so common in David's psalms, Aben Ezra is of opinion it is not his, but written by the singers. This is not a sufficient objection: and besides, in Psalm 66:13, the singular number is used. The Arabic version ascribes it to David, and that version makes the subject matter of it to be "concerning the resurrection"; as do the Septuagint, Ethiopic, and Vulgate Latin versions. The title of the Syriac version is,
"concerning sacrifices and burnt offerings, and the incense of rams; the spiritual sense intimates to us the calling of the Gentiles, and the preaching, that is, of the Gospel;''
which comes nearest the truth: for the psalm respects Gospel times, and the church of Christ under the New Testament, spread throughout the world, and especially as it will be in the latter day; see Psalm 66:1; and so in Yalkut Simeoni on the psalm, it is said to be a psalm for time to come, and agrees with Zephaniah 3:9; "I will turn to the people a pure language", &c. Kimchi says it is a psalm concerning the gathering of the captives of Israel; and so Jarchi and Obadiah expound it; and Theodoret says David wrote this psalm for the captives in Babylon.

(Psalm 66:1-7) Praise for God's sovereign power in the creation.
(Psalm 66:8-12) For his favour to his church.
(Psalm 66:13-20) And the psalmist's praise for his experience of God's goodness.

Thanksgiving for a National and Personal Deliverance
From Psalm 65:1-13 onwards we find ourselves in the midst of a series of Psalm which, with a varying arrangement of the words, are inscribed both מזמור and שׁיר (Ps 65-68). The two words שׁיר מזמור stand according to the accents in the stat. constr. (Psalm 88:1), and therefore signify a Psalm-song.
(Note: If it were meant to be rendered canticum psalmus (not psalmi) it would surely have been accented למנצּח שׁיר מזמור (for למנצח שׁיר מזמור, according to section xviii. of the Accentuationssystem).)
This series, as is universally the case, is arranged according to the community of prominent watchwords. In Psalm 65:2 we read: "To Thee is the vow paid," and in Psalm 66:13 : "I will pay Thee my vows;" in Psalm 66:20 : "Blessed be Elohim," and in Psalm 67:8: "Elohim shall bless us." Besides, Ps 66 and Psalm 67:1-7 have this feature in common, that למנצח, which occurs fifty-five times in the Psalter, is accompanied by the name of the poet in every instance, with the exception of these two anonymous Psalm. The frequently occurring Sela of both Psalm also indicates that they were intended to have a musical accompaniment. These annotations referring to the temple-music favour the pre-exilic rather than the post-exilic origin of the two Psalm. Both are purely Elohimic; only in one instance (Psalm 6:1-10 :18) does אדני, equally belonging to this style of Psalm, alternate with Elohim.
On the ground of some deliverance out of oppressive bondage that has been experienced by Israel arises in Psalm 66 the summons to the whole earth to raise a shout of praise unto God. The congregation is the subject speaking as far as Psalm 66:12. From Psalm 66:13 the person of the poet appears in the foreground; but that which brings him under obligation to present a thank-offering is nothing more nor less than that which the whole congregation, and he together with it, has experienced. It is hardly possible to define this event more minutely. The lofty consciousness of possessing a God to whom all the world must bow, whether cheerfully or against its will, became strong among the Jewish people more especially after the overthrow of Assyria in the reign of Hezekiah. But there is no ground for conjecturing either Isaiah or Hezekiah to be the composer of this Psalm. If עולם in Psalm 66:7 signified the world (Hitzig), then he would be (vid., Psalm 24:9) one of the latest among the Old Testament writers; but it has the same meaning here that it has everywhere else in Old Testament Hebrew.
In the Greek Church this Psalm is called Ψαλμὸς ἀναστάσεως; the lxx gives it this inscription, perhaps with reference to Psalm 66:12, ἐξήγαγες ἡμᾶς εἰς ἀναψυχήν.