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Apostleship is an office in the Melchizedek Priesthood.
- We now have in the restored Church apostles, prophets, pastors, teachers, and evangelists, as spoken of by Paul to the Ephesians. These priesthood offices were established by the Savior when He organized His Church in the meridian of time. Thus those possessing the priesthood today claim the power to act in the name of God through the priesthood, “which power commands respect both on earth and in heaven.” 
Currently, there are 15 apostles on the earth comprising the First Presidency and the Quorum of the Twelve Apostles. Members of the Quorum of the Twelve Apostles are also prophets, seers, and revelators. They, along with the First Presidency, are "special witnesses of the name of Christ in all the world" (Doctrine and Covenants 107:23). They act under the direction of the First Presidency "to build up the church, and regulate all the affairs of the same in all nations" (Doctrine and Covenants 107:33). They "open the door [to the nations] by the proclamation of the gospel of Jesus Christ" (Doctrine and Covenants 107:35).
- The [ancient] apostolic and prophetic foundation of the Church was to bless in all times, but especially in times of adversity or danger, times when we might feel like children, confused or disoriented, perhaps a little fearful, times in which the devious hand of men or the maliciousness of the devil would attempt to unsettle or mislead. Against such times as come in our modern day, the First Presidency and Quorum of the Twelve are commissioned by God and sustained by you as prophets, seers, and revelators, with the President of the Church sustained as the prophet, seer, and revelator, the senior Apostle, and as such the only man authorized to exercise all of the revelatory and administrative keys for the Church. In New Testament times, in Book of Mormon times, and in modern times these officers form the foundation stones of the true Church, positioned around and gaining their strength from the chief cornerstone, “the rock of our Redeemer, who is [Jesus] Christ, the Son of God,” He who is the great “Apostle and High Priest of our profession,” to use Paul’s phrase. Such a foundation in Christ was and is always to be a protection in days “when the devil shall send forth his mighty winds, yea, his shafts in the whirlwind, yea, when all his hail and his mighty storm shall beat upon you.” In such days as we are now in—and will more or less always be in—the storms of life “shall have no power over you … because of the rock upon which ye are built, which is a sure foundation, a foundation whereon if men build they cannot fall.” 
The Lord said to Thomas B. Marsh when he was called as President of the Twelve Apostles:
- Now, I say unto you, and what I say unto you, I say unto all the Twelve: Arise and gird up your loins, take up your cross, follow me, and feed my sheep.
- And again, I say unto you, that whosoever ye shall send in my name, by the voice of your brethren, the Twelve, duly recommended and authorized by you, shall have power to open the door of my kingdom unto any nation whithersoever ye shall send them” (Doctrine and Covenants 112:14, 21).
As of April 2018, the Apostles of The Church of Jesus Christ of Latter-day Saints are as follows: M. Russell Ballard, Jeffrey R. Holland, Dieter F. Uchtdorf, David A. Bednar, Quentin L. Cook, D. Todd Christofferson, Neil L. Andersen, Ronald A. Rasband, Gary E. Stevenson, Dale G. Renlund, Gerrit W. Gong, and Ulisses Soares.
Apostles hold "priesthood keys" to administer the affairs of God on earth. They are prophets, seers, and revelators who have the power and authority to perform the same administrative tasks, and indeed, the same miracles as the apostles who led the Church anciently. They also have the power and authority to perform ordinances that will be sealed in heaven as they are sealed on earth and to ordain others to their ministries in the service of God for the building up of God's kingdom on earth.
By 70 A.D. the ancient apostles of the Lord Jesus Christ had been martyred, and the authority they had held was lost from the earth. Mormons call the ensuing years the "great apostasy," because revelation was not received by religious leaders for a period of time in order to guide the Church. That said, revelation has never ceased. Even after the original apostles died, there were prophets with apostolic authority in the Americas among the Book of Mormon peoples, and presumably among the Ten Lost Tribes, whom Christ visited after His ascension. Because of this loss of apostolic authority to establish the kingdom of God on earth, a restoration of such authority was needed. The restoration of the Aaronic Priesthood came first, then the restoration of the higher, or Melchizedek Priesthood followed. The authority of the Aaronic Priesthood was conferred upon Joseph Smith and Oliver Cowdery by the resurrected John the Baptist; the Melchizedek Priesthood was conferred upon the same two men by Peter, James, and John the Beloved. Keys for taking the gospel to the world, gathering Israel, and the sealing power were conferred by Elias, Moses, and Elijah.
- James E. Faust, “The Restoration of All Things,” Ensign, May 2006, 61–62, 67–68.
- Gospel Topics:Church Administration, lds.org
- Jeffrey R. Holland, “Prophets, Seers, and Revelators,” Liahona, Nov 2004, 6–9.
- Learn more at MormonBible.org