31:33 Under the old covenant, the law of God was engraved on tablets of stone and placed in the Most Holy Place; under the new covenant God will write His law on the hearts of His people. The people then are like the temple in that the law of God is within them, but with the difference that they are a living temple, made of living stones (2 Cor. 3:3; 1 Pet. 2:5). See “God’s Covenant of Grace” at Gen. 12:1.

after those days. The prophet speaks of a time after exile, without being specific. The New Testament shows that the time arrived with Christ, the Messiah.

I will. God will take the initiative to renew His people.

my law. The law of Moses required obedience from the heart (Deut. 6:6) but provided no enablement for that obedience (Deut. 5:29; 29:4). It did mediate forgiveness and hope, especially through the sacrifices. The law was a system of “types and shadows,” that is, of significant elements foreshadowing Christ and inviting trust in God through Him.

I will be their God, and they . . . my people. This declaration is the summary of God’s blessings promised in His covenant (Lev. 26:12; cf. 7:23).