(Church history from official sources)
Given the sensitivity of the topic, it is no surprise that clear references to plural marriage are virtually absent from Joseph Smith’s Nauvoo journals. Some entries, however, may be best understood—or at least partially understood—in light of the practice, although a significant amount of ambiguity remains even after a careful examination of the context and supporting sources. For example, a revelation dated 2 December 1841 for Marinda Nancy Johnson Hyde (recorded in a 25 January 1842 entry of Smith’s journal) closes by counseling her to “hearken to the counsel of my servant Joseph in all things whatsoever he shall teach unto her, and it shall be a blessing upon her and upon her children after her.” Decades later, Hyde reported that this revelation had been delivered to her shortly after Joseph Smith had taught her the “doctrine of celestial marriage” and that she “followed the council of the prophet Joseph as above instructed” and continued to hope for “the fulfilment of the promises and blessings” contained in the revelation. In addition, a 1 May 1869 affidavit signed by Hyde attests that she was “married or sealed” to Joseph Smith in May 1843. Assuming Hyde’s memory accurately reflects events of 1841–1843 and that the “doctrine of celestial marriage” about which she learned included plural marriage, it would be reasonable to conclude that the revelation’s reference to “all things whatsoever” Smith would teach her included a marriage or sealing to the Mormon leader. But Joseph Smith could have counseled Hyde about many other issues in 1841 as well. Her husband, Orson Hyde of the Quorum of the Twelve, for example, had left on a mission to Europe and the Middle East in April 1840, leaving Hyde and her children to rely on others for much of their support until his return in December 1842.

Several later documents suggest that several women who were already married to other men were, like Marinda Hyde, married or sealed to Joseph Smith. Available evidence indicates that some of these apparent polygynous/polyandrous marriages took place during the years covered by this journal. At least three of the women reportedly involved in these marriages—Patty Bartlett Sessions, Ruth Vose Sayers, and Sylvia Porter Lyon—are mentioned in the journal, though in contexts very much removed from plural marriage. Even fewer sources are extant for these complex relationships than are available for Smith’s marriages to unmarried women, and Smith’s revelations are silent on them. Having surveyed the available sources, historian Richard L. Bushman concludes that these polyandrous marriages—and perhaps other plural marriages of Joseph Smith—were primarily a means of binding other families to his for the spiritual benefit and mutual salvation of all involved.

http://josephsmithpapers.org/doc/introduction-to-journals-volume-2

Linked from LDS.org (first result in search for "polyandrous marriages"):
http://www.lds.org/search?lang=eng&query=polyandrous+marriages