Gordon B. Hinckley, the 15th President of The Church of Jesus Christ of Latter-day Saints, made the following statement in 1998 about the Church’s position on plural marriage:
This Church has nothing whatever to do with those practicing polygamy. They are not members of this Church…. If any of our members are found to be practicing plural marriage, they are excommunicated, the most serious penalty the Church can impose. Not only are those so involved in direct violation of the civil law, they are in violation of the law of this Church. 
There have been times when the Lord has commanded His people to practice polygamy (plural marriage.) For example, as taught in modern day revelation in Doctrine and Covenants 132:1, the Lord gave this command to Abraham, Isaac, Jacob, Moses, David, and Solomon. In Doctrine and Covenants (D&C) 132:1 are recorded these words:
Verily, thus saith the Lord unto you my servant Joseph, that inasmuch as you have inquired of my hand to know and understand wherein I, the Lord, justified my servants Abraham, Isaac, and Jacob, as also Moses, David and Solomon, my servants, as touching the principle and doctrine of their having many wives and concubines.
There have been other times when the Lord has given other instructions to his servants. For example, in The Book of Mormon, the Lord told the prophet Jacob as recorded in Jacob 2:27-29:
Wherefore, my brethren, hear me, and hearken to the word of the Lord: For there shall not any man among you have save it be one wife; and concubines he shall have none; for I, the Lord God, delight in the chastity of women. And whoredoms are an abomination before me; thus saith the Lord of Hosts. Wherefore, this people shall keep my commandments, saith the Lord of Hosts, or cursed be the land for their sakes.
The questions then begs to be asked, “How can Latter-day Saints claim to follow the Book of Mormon when it specifically forbids having more than one wife?” Those who pose this question often ask it based on the aforementioned scriptures in Jacob 2:27-29 because they do not fully understand the context. From just these three verses it seems obvious that the Nephites were not to have more than one wife. However, there is one exception, and only one exception, to this rule. To fully understand it requires reading the next verse. Verse 30 of Jacob 2 states:
For if I will, saith the Lord of Hosts, raise up seed unto me, I will command my people; otherwise they shall hearken unto these things.
Stephen R. Gibson, author of One Minute Answers to Anti-Mormon Questions stated:
The one exception would be if the Lord commands his people to live otherwise–to raise up a righteous seed– as he did in Old Testament times as well as in the early days of the Restored Church. Today we continue to live as we have been commanded by the Lord through His prophets; that is, with one wife for each man.
It is interesting that nowhere in the Bible is there wholesale condemnation of the practice of plural marriage. In fact, many of the great men venerated by Christianity had more than one wife: David, Solomon, Abraham, Isaac, Jacob, and many others. As we attempt to understand the doctrine of plural marriage, perhaps it would be helpful to remember that the Lord sent his Only Begotten Son through polygamous lines (Abraham, Isaac, and Jacob). Surely that fact alone indicates the Lord’s approval of this practice when he commands it.
The God of Abraham, Isaac and Jacob is a God who upon occasion gives more than one wife to a righteous man. Obviously, God has different rules and policies for different times. Plural marriage is righteous and acceptable conduct if God commands it through his prophet, but it is an abomination when the Lord has not commanded it. (Stephen R. Gibson, One Minute Answers to Anti-Mormon Questions, pg. 35-36)
In this dispensation, the Lord commanded some of the early Saints to practice plural marriage. The Prophet Joseph Smith and those closest to him, including Brigham Young and Heber C. Kimball, were challenged by this command, but they obeyed it. Church leaders regulated the practice. Those entering into it had to be authorized to do so, and the marriages had to be performed through the sealing power of the priesthood. In 1890, President Wilford Woodruff received a revelation that the leaders of the Church should cease teaching the practice of plural marriage (Official Declaration 1.)