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Plural marriage is as old as the Bible. Abraham and Jacob each had more than one wife. King David had six. King Solomon had 700 (not to mention 300 concubines).
Solomon lost God's favor when he married women who did not give up idolatry, David when he sent a woman's husband to the front lines so he could marry her.
Whether ancient or modern, polygamous or monogamous, marriage has rules. There may be ages and genders to consider. In early America, there were races to consider. Often, those considerations draw on religious beliefs: The Quran allows a man to take up to four wives. In Fundamentalist Mormonism, there is no set limit to the number of wives in one marriage. Joseph Smith, the Mormon Prophet who first delivered God's directive that Mormons practice plural marriage, ultimately took dozens of wives.
In the United States, Fundamentalist Mormons are the most common groups to practice polygamy (although some Neopagans, Liberal Christians and some others also do). For Mormons, polygamy is the Divine Principle, reflecting God's wish that his people are "fruitful and multiply." Mainstream Mormons, members of the Church of Jesus Christ of Latter Day Saints (LDS), officially stopped practicing the Principle in the late 1800s. Those who continued forming plural marriages were eventually excommunicated and became the Fundamentalist Mormons, which include various sects including the FLDS, the AUB, the Priesthood Work and the Independent Fundamentalists not associated with any particular group.
There are actually quite a few different sects that fall under the heading "Fundamentalist Mormon," and distinguishing between them can be helpful in understanding how polygamy is practiced by the group. The lines connecting the sects can be a bit difficult to sort out…