A Commentary, Critical, Practical, and Explanatory on the Old and New Testaments, by Robert Jamieson, A.R. Fausset and David Brown  at sacred-texts.com
psa 72:1For, or literally, "of Solomon." The closing verse rather relates to the second book of Psalms, of which this is the last, and was perhaps added by some collector, to intimate that the collection, to which, as chief author, David's name was appended, was closed. In this view, these may consistently be the productions of others included, as of Asaph, sons of Korah, and Solomon; and a few of David's may be placed in the latter series. The fact that here the usual mode of denoting authorship is used, is strongly conclusive that Solomon was the author, especially as no stronger objection appears than what has been now set aside. The Psalm, in highly wrought figurative style, describes the reign of a king as "righteous, universal, beneficent, and perpetual." By the older Jewish and most modern Christian interpreters, it has been referred to Christ, whose reign, present and prospective, alone corresponds with its statements. As the imagery of the second Psalm was drawn from the martial character of David's reign, that of this is from the peaceful and prosperous state of Solomon's. (Psa. 72:1-19)
Give the king, &c.--a prayer which is equivalent to a prediction.
judgments--the acts, and (figuratively) the principles of a right government (Joh 5:22; Joh 9:39).
righteousness--qualifications for conducting such a government.
king's son--same person as a king--a very proper title for Christ, as such in both natures.
psa 72:2The effects of such a government by one thus endowed are detailed.
thy people . . . and thy poor--or, "meek," the pious subjects of his government.
psa 72:3As mountains and hills are not usually productive, they are here selected to show the abundance of peace, being represented as
bringing--or, literally, "bearing" it as a produce.
by righteousness--that is, by means of his eminently just and good methods of ruling.
psa 72:4That peace, including prosperity, as an eminent characteristic of Christ's reign (Isa 2:4; Isa 9:6; Isa 11:9), will be illustrated in the security provided for the helpless and needy, and the punishment inflicted on oppressors, whose power to injure or mar the peace of others will be destroyed (compare Isa 65:25; Zac 9:10).
children of the needy--for the needy (compare sons of strangers, Psa 18:45 [Margin]).
psa 72:5as long as . . . endure--literally, "with the sun," coeval with its existence, and before, or, in presence of the moon, while it lasts (compare Gen 11:28, "before Terah," literally, "in presence of," while he lived).
psa 72:6A beautiful figure expresses the grateful nature of His influence;
psa 72:7and, carrying out the figure, the results are described in an abundant production
psa 72:8The foreign nations mentioned (Psa 72:9-10) could not be included in the limits, if designed to indicate the boundaries of Solomon's kingdom. The terms, though derived from those used (Exo 23:31; Deu 11:24) to denote the possessions of Israel, must have a wider sense. Thus, "ends of the earth" is never used of Palestine, but always of the world (compare Margin).
psa 72:9The extent of the conquests.
They that dwell in the wilderness--the wild, untutored tribes of deserts.
bow . . . dust--in profound submission. The remotest and wealthiest nations shall acknowledge Him (compare Psa 45:12).
psa 72:12They are not the conquests of arms, but the influences of humane and peaceful principles (compare Isa 9:7; Isa 11:1-9; Zac 9:9-10).
psa 72:15In his prolonged life he will continue to receive the honorable gifts of the rich, and the prayers of his people shall be made for him, and their praises given to him.
psa 72:16The spiritual blessings, as often in Scripture, are set forth by material, the abundance of which is described by a figure, in which a "handful" (or literally, "a piece," or small portion) of corn in the most unpropitious locality, shall produce a crop, waving in the wind in its luxuriant growth, like the forests of Lebanon.
they of the city . . . earth--This clause denotes the rapid and abundant increase of population--
the city--Jerusalem, the center and seat of the typical kingdom.
flourish--or, glitter as new grass--that is, bloom. This increase corresponds with the increased productiveness. So, as the gospel blessings are diffused, there shall arise increasing recipients of them, out of the Church in which Christ resides as head.
psa 72:17His name--or, "glorious perfections."
as long as the sun--(Compare Psa 72:5).
men shall be blessed-- (Gen 12:3; Gen 18:18).
psa 72:18These words close the Psalm in terms consistent with the style of the context, while Psa 72:20 is evidently, from its prosaic style, an addition for the purpose above explained [see on Psa 72:1].
psa 72:20ended--literally, "finished," or completed; the word never denotes fulfilment, except in a very late usage, as in Ezr 1:1; Dan 12:7.