This psalm is one of those which in the title are ascribed to Asaph (see Introduction to Ps. 73), and there is no reason to call in question that statement. On the phrase "To the chief Musician on Neginoth," see Introduction to Psalm 4:1-8.
The occasion on which the psalm was composed is not stated, and cannot now be ascertained. The Septuagint regards it as having had reference to the Assyrians - ᾠδὴ προς τὸν Ἀσσύριον hōdē pros ton Assurion - "An ode to the Assyrian." So the Latin Vulgate; Canticum ad Assyrios. This is the opinion adopted also by Jarchi. The title in the Syriac version is, "When Rabbah of the Ammonites was laid waste; and further it describes the judment of the Messiah against the wicked. Grotius supposes that it was intended to describe the victory over the Ammonites. Rudinger ascribes its composition to the time of the Maccabees. DeWette supposes that it refers to some late period of the Jewish history, but that the particular time is unknown. It would be vain to attempt to ascertain with any certainty the particular occasion on which the psalm was composed. It was evidently on some occasion when an attack had been made on "Salem," that is, on Jerusalem Psalm 76:2-3, and when that attack had been repelled, and the enemy had been driven back. Many of the circumstances in the psalm. would agree well with the account of the invasion of the Assyrians under Sennacherib, but there were many other occasions in the Jewish history to which it would, in like manner, be applicable.
The psalm is a song of praise for deliverance from an enemy. The contents are as follows:
I. The fact that God had made himself known "in Judah," or to the Jewish people - or, that he had manifested himself to them in a remarkable manner, Psalm 76:1.
II. The fact that he had showed this in a special manner in "Salem," the capital of the nation - referring to some particular time in which this was done, Psalm 76:2.
III. The manner in which he had done this - by breaking the arrows of the bow, and the shield; by showing that his power was superior to all the defenses which men had set up; and by overcoming entirely the invading foe, Psalm 76:3-6.
IV. The fact that, on this account, God was to be feared and reverenced, Psalm 76:7-9.
V. The statement of a great truth, and a most important principle, which had been particularly illustrated by the occurrence; to wit, that the wrath of man would be made to praise God, and that the remainder of wrath he would restrain, Psalm 76:10.
VI. A call on all people to acknowledge God in a suitable manner, by bringing presents, and by standing in awe of him, Psalm 76:11-12.

The true God known in Judah, Israel, Salem, and Zion, Psalm 76:1, Psalm 76:2. A description of his defeat of the enemies of his people, Psalm 76:3-6. How God us to be worshipped, Psalm 76:7-9. He should be considered as the chief Ruler: all the potentates of the earth are subject to him, Psalm 76:10-12.
The title, "To the chief Musician on Neginoth, a Psalm or Song of Asaph." Sae the titles to Psalm 4:1-8 : and 6: The Vulgate, Septuagint, and others have, "A Psalm for the Assyrians;" and it is supposed to be a thanksgiving for the defeat of the Assyrians. The Syriac says it is a thanksgiving for the taking of Rabbah, belonging to the children of Ammon. It is considered by some of the best commentators to have been composed after the defeat of Sennacherib. That it was composed after the death of David, and after the two kingdoms of Israel and Judah were separated, is evident from the first verse. If Asaph was its author, it could not be the Asaph that flourished in the days of David but some other gifted and Divinely inspired man of the same name, by whom several others of the Psalm appear to have been composed during the captivity.

INTRODUCTION TO PSALM 76
To the chief Musician on Neginoth, A Psalm or Song of Asaph. The Targum is,
"by the hand of Asaph:''
concerning "neginoth", see the title of Psalm 4:1, this psalm is generally thought to be written on account of some great appearance of God for the Jews, or victory obtained by them over their enemies, either the Ammonites in the times of David; so the first part of the Syriac inscription is,
"when Rabbah of the children of Ammon was destroyed;''
see 2-Samuel 12:26 or in the time of Jehoshaphat, when they came up against him, and were in a wonderful manner defeated, which occasioned great joy and thankfulness, 2-Chronicles 20:1. The Septuagint version entitles the psalm "an ode against the Assyrian", in which it is followed by the Vulgate Latin and Ethiopic versions: and it is the opinion of many that it was written on account of the defeat of Sennacherib, and his army, which came up against Jerusalem in the times of Hezekiah, and was destroyed by an angel in one night, and so slept their sleep, and a dead one, with which agree Psalm 76:5, so Arama and Theodoret; Jarchi gives this reason for such an interpretation, because we do not find that any enemy fell at or near Jerusalem but he, as is said Psalm 76:3, "there brake he the arrows of the bow", &c. nor was one arrow suffered to be thrown into the city, 2-Kings 19:32. Kimchi and Ben Melech interpret it of the war of Gog and Magog, yet to come; and the latter part of the Syriac inscription is,
"moreover it shows the vengeance of the judgment of Christ against the ungodly;''
and indeed it seems to point out the latter day, when Christ shalt destroy the antichristian kings and states, and save his own people, and shall be feared and praised; as the former part of it may respect his incarnation, appearance, and dwelling in the land of Judea, and so the whole is of the same argument with the preceding psalm.

(Psalm 76:1-6) The psalmist speaks of God's power.
(Psalm 76:7-12) All have to fear and to trust in him.

Praise of God after His Judgment Has Gone Forth
No Psalm has a greater right to follow Psalm 75:1-10 than this, which is inscribed To the Precentor, with accompaniment of stringed instruments (vid., Psalm 4:1), a Psalm by Asaph, a song. Similar expressions (God of Jacob, Psalm 75:10; Psalm 76:7; saints, wicked of the earth, Psalm 75:9; Psalm 76:10) and the same impress throughout speak in favour of unity of authorship. In other respects, too, they form a pair: Psalm 75:1-10 prepares the way for the divine deed of judgment as imminent, which Psalm 76:1-12 celebrates as having taken place. For it is hardly possible for there to be a Psalm the contents of which so exactly coincide with an historical situation of which more is known from other sources, as the contents of this Psalm confessedly (lxx πρὸς τὸν Ἀσσύριον) does with the overthrow of the army of Assyria before Jerusalem and its results. The Psalter contains very similar Psalm which refer to a similar event in the reign of Jehoshaphat, viz., to the defeat at that time of the allied neighbouring peoples by a mutual massacre, which was predicted by the Asaphite Jahaziel (vid., on Psalm 46:1-11 and Ps 83). Moreover in Psalm 76:1-12 the "mountains of prey," understood of the mountains of Seir with their mounted robbers, would point to this incident. But just as in Psalm 75:1-10 the reference to the catastrophe of Assyria in the reign of Hezekiah was indicated by the absence of any mention of the north, so in Psalm 76:1-12 both the שׁמּה in Psalm 76:4 and the description of the catastrophe itself make this reference and no other natural. The points of contact with Isaiah, and in part with Hosea (cf. Psalm 76:4 with Hosea 2:20) and Nahum, are explicable from the fact that the lyric went hand in hand with the prophecy of that period, as Isaiah predicts for the time when Jahve shall discharge His fury over Assyria, Isaiah 30:29, "Your song shall re-echo as in the night, in which the feast is celebrated."
The Psalm is hexastichic, and a model of symmetrical strophe-structure.