A Steady Blaze

J. I. Packer explains what God’s wrath is and to whom it applies:

The biblical idea of the wrath of is well defined by James Orr: it is ‘an energy of the divine nature called forth by the presence of daring or presumptuous transgression, and expressing the reaction of the divine holiness against it in the punishment or destruction of the transgressor. It is the ‘zeal” of God for the maintenance of holiness and honour, and of the ends of His righteousness and love, when these are threatened by ingratitude, rebellion and wilful disobedience or temerity of the creature’ (Hastings’ Dictionary of the Bible, 1, pp. 77f.). God’s wrath against sin is not a fitful flicker, but a steady blaze; not a mark of uncertain temper, but an aspect of the consistent righteousness of the just Judge of all the earth. to this hostile reaction of God, Paul tells us, all sinners, as such, are exposed. The first truth expounded in Romans is that ‘the wrath of God is revealed from heaven against all ungodliness and wickedness of men’ (Rom. 1:18). The background of the good news of grace is the bad news of judgment; the context within which the New Testament announces God’s reconciling mercy is the declaration of His active wrath. Men are opposed to God in their sin, and God is opposed to men in His holiness. Those who are under the rule of sin are also under the wrath of God. It is against the dark backcloth of this view of the natural relations of man and his Maker that the gospel of reconciliation is expounded.

From the chapter on reconciliation in 18 Words: The Most Important Words You Will Ever Know.