Mormon Polygamy

The Mormon leadership was introduced to the concept of polygamy as earl as 1831, just a year after the Church was restored.  However it was not practiced for some time.  When it was first practiced, it was not open, and so many rumors circulated about sexual impropriety.  The revelation dealing with plural marriage was recorded in 1843.  Polygamy was announced openly for the first time at the autumn conference of 1852, with Orson Pratt giving a sermon to the conference.  Shortly after this, polygamy was an open doctrine through the church. 
To most of the world, Mormon polygamy was lascivious men seeking a harem.  This could not be further from the truth.  Polygamy was exercised only on the spirit of revelation, and only with permission from ecclesiastical leaders.  Men who entered polygamy did not do so to satisfy sexual urges, but to satisfy religious and spiritual urges.  They were gaining their own personal salvation by entering into polygamy.  It is true, not all peoples are required to obey the law of polygamy.  However, for whatever reason, many of the church were asked to enter into polygamy at this time.  Jacob of the Book of Mormon gives a possible reason for this.  After telling the people they should have only one wife, he explains: Jacob 2:30 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.  Those who entered polygamy, men and women, had as their goad to raise a righteous generation to the Lord.  They were successful in this.
In 1862 the Morrill Act outlawed polygamy in the territories.  However this was not enforced at the time.  Mormons felt this law violated their religious liberties, and was unconstitutional.  However in 1879 the Supreme Court ruled it was constitutional.  In 1882 the Edmunds Act was passed.  This imposed stricter penalties, and initiated "The Raid" as Mormons called it--an onslaught of federal marshals who were seeking polygamist men (or cohabs as they were called) with the goal of putting them in jail, or their being fined.  The marshal received a bounty for every polygamist they were able to bring in.
The law wasn't effective in ending the practice.  Too many men escaped capture.  Those that were captured served their time, and returned folk heroes.  In 1879 the Edmunds Tucker Act went after the church itself.  Although the church had already been attacked and dis-incorporated, this act arranged for the transfer of church property to the church.  This included the temples. 
In 1890 Wilford Woodruff announced the Manifesto, which ended church support for polygamy.  There were still issues to be worked out, but the Church's official position today is that those who practice polygamy are caught off from the church.  There are splinter groups practicing polygamy, but for a church member to practice polygamy would result in their excommunication.
Bibliography
http://bwardlehistory.blogspot.com/2014/01/mormon-polygamy-biography.html