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 79:1This Psalm, like the seventy-fourth, probably depicts the desolations of the Chaldeans (Jer 52:12-24). It comprises the usual complaint, prayer, and promised thanks for relief. (Psa 79:1-13)
(Compare Psa 74:2-7).
psa 79:2(Compare Jer 15:3; Jer 16:4).
psa 79:4(Compare Psa 44:13; Jer 42:18; Lam 2:15).
psa 79:5How long-- (Psa 13:1).
be angry-- (Psa 74:1-10).
jealousy burn-- (Deu 29:20).
psa 79:6(Compare Jer 10:25). Though we deserve much, do not the heathen deserve more for their violence to us (Jer 51:3-5; Zac 1:14)? The singular denotes the chief power, and the use of the plural indicates the combined confederates.
called upon--or, "by"
thy name--proclaimed Thy attributes and professed allegiance (Isa 12:4; Act 2:21).
psa 79:8former iniquities--literally, "iniquities of former times."
prevent us--literally, "meet us," as in Psa 21:3.
psa 79:9for . . . glory of thy name [and for] thy name's sake--both mean for illustrating Thy attributes, faithfulness, power, &c.
purge . . . sins--literally, "provide atonement for us." Deliverance from sin and suffering, for their good and God's glory, often distinguish the prayers of Old Testament saints (compare Eph 1:7).
psa 79:10This ground of pleading often used (Exo 32:12; Num 14:13-16).
blood . . . shed-- (Psa 79:3).
psa 79:11prisoner--the whole captive people.
power--literally, "arm" (Psa 10:15).
psa 79:12into their bosom--The lap or folds of the dress is used by Eastern people for receiving articles. The figure denotes retaliation (compare Isa 65:6-7). They reproached God as well as His people.
psa 79:13sheep . . . pasture--(Compare Psa 74:1; Psa 78:70).