The Book of Mormon sets monogamy as the rule, as does the Bible. The difference is that the Book of Mormon allows for an exception in cases that are specifically commanded by God. The practice of plural marriage, or polygamy, in Mormonism goes back to Joseph Smith, who in 1843 said he received an eternally binding commandment from God that men should take multiple wives. Official Mormon sources have recently admitted that Smith had as many as 33 wives, although other researchers say they have found evidence for more. His successor, Brigham Young, who had 55 wives, said, “The only men who become gods, even the sons of god, are those who enter into polygamy” (Journal of Discourses), although it seems he held out hope that some could enter heaven without taking multiple wives. Young made this statement as the Mormons were being pressured by the American government and society to abandon the practice of plural marriage. For Young, it was a matter of faith and obedience.
Mormon theology essentially says that God was once like us and that we can become like Him by following Mormon teaching. Faithful Mormon men will one day be exalted to god status and have their own worlds to create and populate. They populate these worlds by having many children, and this will require many wives in heaven. Those “many wives” in heaven need to first be sealed to a husband on earth.
Currently, the official Mormon position supports monogamy. Due to legal and social pressures, Mormon officials banned the practice of plural marriage in 1890; however, many Mormons still participate in plural “spiritual” marriages, which are said to have the same effect in heaven as physical marriages. In this arrangement, a Mormon man lives monogamously with one wife on earth, but he has been spiritually sealed to many other women who will be available to him in heaven. Of course, there are some “fundamentalist” Mormon groups that still practice plural marriage outright.