Covenant theology is the Gospel set in the context of God’s eternal plan of communion with his people, and its historical outworking in the covenants of works and grace (as well as in the various progressive stages of the covenant of grace). Covenant theology explains the meaning of the death of Christ in light of the fullness of the biblical teaching on the divine covenants, undergirds our understanding of the nature and use of the sacraments, and provides the fullest possible explanation of the grounds of our assurance.
To put it another way, Covenant theology is the Bible’s way of explaining and deepening our understanding of: (1) the atonement [the meaning of the death of Christ]; (2) assurance [the basis of our confidence of communion with God and enjoyment of his promises]; (3) the sacraments [signs and seals of God’s covenant promises — what they are and how they work]; and (4) the continuity of redemptive history [the unified plan of God’s salvation]. Covenant theology is also an hermeneutic, an approach to understanding the Scripture — an approach that attempts to biblically explain the unity of biblical revelation.
When Jesus wanted to explain the significance of His death to His disciples, He went to the doctrine of the covenants (see Matthew 26, Mark 14, Luke 22, 1 Corinthians 11). When God wanted to assure Abraham of the certainty of His word of promise, He went to the covenant (Genesis 12, 15, and 17). When God wanted to set apart His people, ingrain His work in their minds, tangibly reveal Himself in love and mercy, and confirm their future inheritance, He gave the covenant signs (Genesis 17, Exodus 12, 17, and 31, Matthew 28, Acts 2, Luke 22). When Luke wanted to show early Christians that Jesus’ life and ministry were the fulfillment of God’s ancient purposes for His chosen people, he went to the covenants and quoted Zacharias’ prophecy which shows that believers in the very earliest days of ‘the Jesus movement’ understood Jesus and His messianic work as a fulfillment (not a ‘Plan B’) of God’s covenant with Abraham (Luke 1:72-73). When the Psalmist and the author of Hebrews want to show how God’s redemptive plan is ordered and on what basis it unfolds in history, they went to the covenants (see Psalm 78, 89, Hebrews 6-10).
Covenant theology is not a response to dispensationalism. It existed long before the rudiments of classical dispensationalism were brought together in the nineteenth century. Covenant theology is not an excuse for baptizing children, nor merely a convention to justify a particular approach to the sacraments (modern paedocommunionism and baptismal regenerationism). Covenant theology is not sectarian, but an ecumenical Reformed approach to understanding the Bible, developed in the wake of the magisterial Reformation, but with roots stretching back to the earliest days of catholic Christianity and historically appreciated in all the various branches of the Reformed community (Baptist, Congregationalist, Independent, Presbyterian, Anglican, and Reformed). Covenant theology cannot be reduced to serving merely as the justification for some particular view of children in the covenant (covenant successionism), or for a certain kind of eschatology, or for a specific philosophy of education (whether it be homeschooling or Christian schools or classical schools). Covenant theology is bigger than that. It is more important than that.
“The doctrine of the covenant lies at the root of all true theology. It has been said that he who well understands the distinction between the covenant of works and the covenant of grace, is a master of divinity. I am persuaded that most of the mistakes which men make concerning the doctrines of Scripture, are based upon fundamental errors with regard to the covenant of law and of grace. May God grant us now the power to instruct, and you the grace to receive instruction on this vital subject.” Who said this? C.H. Spurgeon — the great English Baptist preacher! Certainly a man beyond our suspicion of secretly purveying a Presbyterian view of the sacraments to the unsuspecting evangelical masses.
Covenant theology flows from the trinitarian life and work of God. God’s covenant communion with us is modeled on and a reflection of the intra-trinitarian relationships. The shared life, the fellowship of the persons of the Holy Trinity, what theologians call perichoresis or circumincessio, is the archetype of the relationship the gracious covenant God shares with His elect and redeemed people. God’s commitments in the eternal covenant of redemptive find space-time realization in the covenant of grace.
You can also check out Introduction: On Covenant Theology by J.I. Packer and Monergism has a great collection of resources on Covenant Theology
Michael Horton has a great introductory book on this topic called, Introducting Covenant Theology