This is a historical misnomer. Brother Joseph Smith was only married to Emma. There is not on e single shred of credible historical evidence that he had 40 to 80 other wives. While it is " really cool" in some circles to say that he did, there is no basis in fact. It is such a treasured myth, most people will not even consider it that he was only married to Emma.
Members of the Church of Jesus Christ of Latter-day Saints (the
"Mormon" church) discontinued the practice of polygamy over 110
years ago, but some calling themselves "Mormon Fundamentalists"
continue the practice, although they are not affiliated with the
mainstream Mormon church.
All Mormon groups (polygamist or not) are "Restorationist Christian" meaning they believe their religion to be the ancient Biblical religion restored (as opposed to continued or reformed) in modern times. Since polygamy was practiced by the prophets of the Old Testament, it logically follows that should be a part of a modern church which claims to be the same as that found in the Bible.
The founder of the Mormonism movement, Joseph Smith, received revelations restoring the practice of polygamy which he made public in 1843. In these revelations, after recounting the Old Testament practice, God declares, "I am the Lord thy God, and I gave unto thee, my servant Joseph, an appointment, and restore all things... if any man espouse a virgin, and desire to espouse another, and the first give her consent, and if he espouse the second, and they are virgins, and have vowed to no other man, then is he justified." (See Doctrine& Covenants sec. 132)
The mainstream Mormon Church discontinued the practice of polygamy in 1890 (in the United States) and 1903 (internationally), as the (then) prophet Wilford Woodruff declared: "Inasmuch as laws have been enacted by Congress forbidding plural marriages, which laws have been pronounced constitutional by the court of last resort, I hereby declare my intention to submit to those laws, and to use my influence with the members of the Church over which I preside to have them do likewise." (see Official Declaration 1) The abandonment of the practice caused quite a stir, even causing some top church officials to leave their posts. Many supporters of polygamy declared Woodruff a fallen prophet and left the Church, some organizing their own churches. This gave birth to the modern "Mormon Fundamentalist" movement.