In the general sense, a covenant is simply a binding agreement or compact between two or more parties; in legal terms, it is a formal sealed agreement or contract.
Classically, covenants are between nations or other powerful groups (for example, 1 Samuel 11:1; Joshua 9:6,15). At the international level they usually involve an alliance between two unequal parties - the stronger one pledging protection and help to the weaker in return for some form of vassal status (as in vassal treaties).
This is similar to the biblical picture of God’s relationship with his people, except that the inequality between the parties (Creator and creatures) is absolute. It is always made clear that the initiative is God’s - that He makes covenants with his people and not vice versa. God initiates, confirms and even fulfils (ultimately in Christ, both sides of) the covenant.
In the Old Testament the word covenant translates the Hebrew berit. This Hebrew word derives from a root which means "to cut" and hence a covenant is a "cutting" with reference to the ancient custom of cutting or dividing animals into two parts with the contracting parties passing between them, in making a covenant, see for example Jeremiah 34:18-19. Some suggest the parties of the covenant are thereby saying in essence, "May I be torn apart like these animals if I fail to uphold my part of this covenant." This is illustrated in Genesis 15, as God alone passes between the slaughtered animals while Abraham sleeps, again emphasizing the unilateral nature of this covenant, as well as the ultimate level of commitment involved - God putting his very life on line, as it were, as guarantee.
In the New Testament, the Greek word diatheke similarly means covenant, testament, or will. In fact, the Old and New "Testaments" are really the Old and New "Covenants" - the new covenant being of course that which was established by Christ through His shed blood for the remission of sins (Matthew 26:28).
What is so amazing about such examples of covenant then, is that they are the gracious means of relationship with God for a people who deserve to be removed from His presence forever, by a God who has no need whatsoever, in and of Himself, for such relationship. Indeed, the heart of covenant, as so often and wonderfully recapitulated by God Himself is that expression of intimate relationship: "you will be my people, and I will be your God" (e.g. Jeremiah 30:22).
Three crucial aspects of divine covenent have been outlined above: unilateral establishment, relational bond and ultimate commitment. Each of these apsects is brought out in O. Palmer Robertson's definition of covenant as "a bond in blood sovereignly administered".
The nature of God's covenantsEdit
"God's covenants contain two especially important components: terms and duration. Although humans may reach covenants or other agreements through their own devices, God's covenants with people are usually unilateral. He alone determines the terms and conditions; humans choose whether to accept them.
"For example, after God clearly defined aspects of the covenant He was making with the nation of Israel, including the blessings for honoring it and the consequences for ignoring it (Leviticus 26; Deuteronomy 28-30), both parties - God and the people of Israel - accepted it. Through this process God and Israel entered into a covenant relationship, a binding commitment to honor and fulfill their respective roles.
"A second important concept for us to understand about God's covenant with Israel is its continuing relevance to our day. In reaffirming the covenant with the generation of Israelites who were poised to enter the Promised Land, Moses explained that they were doing this "that (God) may establish you today as a people for Himself, and that He may be God to you, just as He has spoken to you, and just as He has sworn to your fathers, to Abraham, Isaac, and Jacob. I make this covenant and this oath, not with you alone, but with him who stands here with us today before the LORD our God, as well as with him who is not here with us today" (Deuteronomy 29:13-15). The covenant clearly applied to Israel's descendants as well." 
Given, on the one hand, the unilateral nature of divine covenant and its gracious and promissory nature, while on the other, the presence of stipulations the question of the conditionality or otherwise of individual covenants is a difficult one, and there is diversity of opinion. John Murray understands the answer to be in the relational aspect of the covenant which when present "implies mutuality" so that the conditions "are simply the reciprocal responses of faith, love and obedience, apart from which the enjoyment of the covenant blessing and of the covenant relation are inconceivable. In a word, keeping the covenant presupposes the covenant relation as established rather than the condition upon which its establishment is contingent" (Murray 19).
- The Noahic Covenant, found in Genesis 8:20-9:17.
- The Abrahamic Covenant, found in Genesis chapter 15.
- The Mosaic Covenant, found in Exodus chapters 19 through 24.
- The Palestinian Covenant -- an unconditional covenant enlarging upon the Abrahamic Covenant promising the seed of Abraham eternal possession in the land (Deuteronomy 30:1-10), and
- The Davidic Covenant, found in 2 Samuel chapter 7 establishing David and his lineage as the rightful kin]s of Israel and Judah and extending the covenant of Abraham to David's lineage.
- The New Covenant, predicted by the prophet Jeremiah in the eponymous book, chapter 31, and connected with Jesus at the Last Supper where he says that the cup is "the New Covenant in [his] blood" and further in the Epistle to the Hebrews (chapters 8-10). The term "New Testament," most often used for the collection of books in the Bible, can also refer to the New Covenant as a theological concept.
- Murray, John (1988). The Covenant of Grace. Phillipsburg: Presbyterian & Reformed.
- Robertson, O. Palmer (1981). Christ of the Covenants. Phillipsburg: Presbyterian & Reformed.
- Horton, Michael (2006). "God of Promise". Grand Rapids: Baker Book House.
- Williams, Michael (2005). "The Covenant Story of Redemption". Phillipsburg: Presbyterian & Reformed.