I’ll add to this post as quotations strike me as unusual or helpful or contain cross-references I don’t want to lose.
From Elder Nelson’s talk “Covenants“
Some of these promises have been fulfilled; others are still pending. I quote from an early Book of Mormon prophecy: “Our father [Lehi] hath not spoken of our seed alone, but also of all the house of Israel, pointing to the covenant which should be fulfilled in the latter days; which covenant the Lord made to our father Abraham.”18 Isn’t that amazing? Some 600 years before Jesus was born in Bethlehem, prophets knew that the Abrahamic covenant would be finally fulfilled only in the latter days.
To facilitate that promise, the Lord appeared in these latter days to renew that Abrahamic covenant. To the Prophet Joseph Smith, the Master declared:
“Abraham received promises concerning his seed, and of the fruit of his loins—from whose loins ye are, … my servant Joseph. …
“This promise is yours also, because ye are of Abraham.”19
With this renewal, we have received, as did they of old, the holy priesthood and the everlasting gospel. We have the right to receive the fulness of the gospel, enjoy the blessings of the priesthood, and qualify for God’s greatest blessing—that of eternal life.20