The Ahmadiyya community is defined by a single claim, and the claim is the reason for everything that has happened to it.
Mirza Ghulam Ahmad, a scholar from Qadian in Punjab, announced from 1889 that he was the reformer promised for the age, and subsequently that he was the Messiah awaited by Christians, the Mahdi awaited by Muslims, and an avatar corresponding to Hindu expectation, one figure fulfilling the promises of several traditions at once. He also taught that Jesus survived the crucifixion, travelled east, and died a natural death in Kashmir, where the community identifies his tomb; and he preached jihad by argument and persuasion rather than by the sword, a position formed in colonial India and directed as much at Christian missionaries as at anyone.
The obstacle is the doctrine of the finality of prophethood. Mainstream Islam holds Muhammad to be the seal of the prophets, after whom none comes. Ahmad's claim was to a subordinate, non-law-bearing prophethood entirely dependent on Muhammad's, which the community argues is compatible with finality. Almost all other Muslim authorities hold that it is not, and that the claim places the movement outside Islam.
The community itself divided over precisely this point after the death of Ahmad's first successor in 1914. The larger Qadiani branch holds Ahmad to be a true if subordinate prophet; the smaller Lahore Ahmadiyya Movement holds him to be a reformer only, and is correspondingly less objectionable to other Muslims, though it has attracted far fewer followers.
Organisationally the community is tightly run, under an elected caliph whose seat moved from Qadian to Pakistan after partition and to London in 1984. It is known for a disciplined financial contribution system, a global broadcasting operation and extensive charitable work.