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Alphabetical
The Church of Jesus Christ of Latter-day Saints
Essential apostle functions:
The calling of an Apostle is to be a special witness of the name of Jesus Christ in all the world, particularly of His divinity and of His bodily resurrection from the dead (Acts 1:22; D&C 107:23). Twelve men with this high calling constitute an administrative council in the work of the ministry.
See also:
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For the vast majority of Christians the term "Apostle" primarily refers to Jesus' chosen 12, their immediate successors, and some others explicitly called Apostles in scripture.
However the term "apostle" simply means one sent by God to preach his truth, and in that sense every Christian can be truthfully called an apostle.
The vast majority of Christian churches do not use the term "Apostle" as a title for a church position.
Some smaller Protestant churches do use the term "Apostle" to describe those with either specific positions in the church or specific ministries. Frequently this refers to either:
Obviously items 1, 2 and 7 cannot apply to modern-day Apostles (unless the church has a open canon, although in practice that rarely applies).
Item 3 applies only to Pentecostal churches (in the widest sense) where most church leaders are expected to exhibit the Gifts of the Spirit. "Mighty deeds" is unlikely to be a qualification for modern day Apostles.