Romans 3:23-24

This is one of the most elementary of proof-texts of the Bible. If we understand it, we understand Christ's work on our behalf. We are saved by grace, through faith in Jesus.

23 πάντες γὰρ ἥμαρτον καὶ ὑστεροῦνται τῆς δόξης τοῦ θεοῦ, 24 δικαιούμενοι δωρεὰν τῇ αὐτοῦ χάριτι διὰ τῆς ἀπολυτρώσεως τῆς ἐν Χριστῷ ᾽Ιησοῦ·

23 for all have sinned and fall short of the glory of God; 24 but they are justified as a gift by his grace, through the redemption that is in Christ Jesus

πάντες γὰρ ἥμαρτον for all have sinned. There is no room in πάντες for any escape; it is a net that catches all of us in our sins. ἥμαρτον is the aorist plural of ἁμαρτάνω; the aorist doesn't pick a moment in time, it just speaks the truth. This simple statement of truth makes all of us guilty before God and worthy of death, and of eternal suffering in hell.

καὶ ὑστεροῦνται τῆς δόξης τοῦ θεοῦ, and fall short of the glory of God; ὑστεροῦνται is a plural passive indicative from ὑστερέω, "to fall short, lack." The passive voice here indicates that we are all lacking, or coming short." δόξης "glory" is that which can be praised; it is the righteousness of God.

Luther said: “Glory of God” is used in the same way as righteousness, wisdom, and virtue, that is, something which is given to us by God and because of which we can before him glory in him and about him.

δικαιούμενοι but they are justified, present passive participle from δικαιόω, "acquit." The passive here means that we have been acquitted; forensically declared to be not guilty of our sins by God himself.

δωρεὰν as a gift, δωρεάν is an adverb, "without cost, for nothing, as a gift." In Galatians 2:21 it means "needlessly," and we could as easily say that here. For no reason, we have been declared innocent of our sins by God.

τῇ αὐτοῦ χάριτι by his grace, The dative here is the simplest dative of all, the dative of means. The way God accomplished this was by means of his grace. Grace (χάρις) is the undeserved good will of God for mankind.

διὰ τῆς ἀπολυτρώσεως through the redemption Just as we had a dative of means, we now have a genitive of means, the means through which God's grace came to us: the "redemption" or "buying back" (ἀπολύτρωσις), the payment made by God himself for us. He paid, and the payment was his son, and the payment was made to himself. But the payment is made, and it is completed on our behalf.

τῆς ἐν Χριστῷ ᾽Ιησοῦ· that is in Christ Jesus. This is a relative clause describing what kind of ἀπολύτρωσις was made: the one that was made within, and only within, the sphere of Christ. Everything Christ did paid the expense for our debt. His active obedience filled up our complete lack of obedience to God. And his passive obedience -- his death -- paid the price for our open and hidden rebellion against God in our sins.

On the order of the name Χριστῷ ᾽Ιησοῦ, Bengel is profound: "According to the Old Testament [from the Old Testament point of view], progress is made from the knowledge of Christ to the knowledge of Jesus; in the experience of present faith [from the New Testament point of view, the progress is] from the knowledge of Jesus to the knowledge of Christ." (Loc. cit.)