Mormons believe in the covenants that God has made with His people through-out history.  We believe that covenants are a two-way promise between God and mankind.  He always keeps His side of the agreement and, to the extent that we keep our part, He blesses us according to the terms of the covenants we make with Him.  Examples of important covenants are the Abrahamic Covenant, the Covenant (or Law) of Moses, the Atonement of Christ, etc.  We do not believe that all of the covenants in the Old Testament have been replaced or superseded by the New Testament.  Some, like the Law of Moses, ended because they were fulfilled completely with the coming of Christ.  Others are still in force.  After his resurrection, the Lord, Jesus Christ explained it in these words:

"Behold, I am he that gave the law, and I am he who covenanted with my people Israel; therefore, the law in me is fulfilled, for I have come to fulfill the law; therefore it hath an end. Behold, I do not destroy the prophets, for as many as have not been fulfilled in me, verily I say unto you, shall all be fulfilled. And because I said unto you that old things have passed away, I do not destroy that which hath been spoken concerning things which are to come. For behold, the covenant which I have made with my people is not all fulfilled; but the law which was given unto Moses hath an end in me."  (Book of Mormon: 3 Nephi 15:5-8)

Mormons believe that ordinances such as baptism, partaking of the sacrament, and marriage are examples of covenants with God.  For a detailed explanation of the covenant that we make with Christ at baptism, please see the answer to the question on Faith and Works.

We believe that our doctrine is a restoration of the fullness of the Gospel in our day, so while we respect the reformers, our beliefs about covenants are not necessarily connected to the reformation movement.  We believe that God speaks to mankind today, that as in times of old, He has appointed prophets and apostles in our day, and that the authority to perform covenant ordinances has been restored to the earth.