Joseph Smith taught that sexual relations were justified and expected in polygamous unions in order "to multiply and replenish the earth" (D&C 132:63). However, evidence is lacking or unpersuasive in four groups: (1) women to whom Joseph Smith was not married; (2) women sealed for the next life only, that is, "eternity" only sealings; (3) in sealings to two fourteen-year-old wives; and (4) in sexual polyandrous situations (plural sealings to women who were civilly married and experiencing connubial relations with their legal husbands).
Even though sexuality was permitted in Joseph Smith's plural marriages, it does not appear that conjugal interactions were a common occurrence. Opportunities for Joseph to spend intimate time with his plural wives would have been limited by many factors including his parenting responsibilities at the Homestead and the Nauvoo Mansion, by his preoccupation with Church and civic matters, by the constant need for secrecy, and by the scrutiny of dissenters and unbelievers.
Emma’s vigilant and mostly intolerant eyes would have been another significant deterrent. Emily Partridge recalled:
We [Emily and Eliza Partridge] were sealed in her [Emma’s] presence with her full and free consent. It was the 11th of May, but before the day was over she turned around or repented of what she had done and kept Joseph up till very late in the night talking to him. She kept close watch of us. If we were missing for a few minutes, and Joseph was not at home, the house was searched from top to bottom and from one end to the other, and if we were not found, the neighborhood was searched until we were found. 
A reminiscences from Joseph Lee Robinson states:
Ebenezer [Robinson]’s wife, [Angeline], had some time before this had watched Brother Joseph the prophet and had seen him go into some house and that she had reported to Sister Emma, the wife of the prophet. It was at a time when she was very suspicious and jealous of him for fear he would get another wife, for she knew the prophet had a revelation on that subject. She (Emma) was determined he should not get another, if he did she was determined to leave and when she heard this, she, Emma, became very angry and said she would leave...
That sexual relations were uncommon is also reflected by the observation that only two or three pregnancies have been mentioned and only one or two that have been documented with any degree of reliability. Mary Elizabeth Rollins Lightner stated: “I know he [Joseph Smith] had three children. They told me. I think two are living today but they are not known as his children as they go by other names.” On another occasion she declared: “I don’t know about his having children, but I heard of three that he was the father of.” Current research supports that one daughter, Josephine Lyon, was born to Sylvia Sessions in 1844 and a child to Olive Frost that did not live long or may have miscarried.
Most of Joseph Smith's plural wives were fertile and young, capable of conception if the timing was right. The Prophet was virile, having fathered nine children with Emma despite their long periods of time apart and challenging schedules.
Antagonists may argue that other children were born to Joseph and his plural wives, but their existence was kept secret. However, decades after the martyrdom when RLDS Church missionaries were claiming that Joseph Smith was not a polygamist, Utah Church authorities aggressively combated their claims. It is probable that if they would have known of any children fathered by the Prophet with his plural wives, they would have publicly acknowledged it.
No convincing evidence has been found to support a third child born to the Prophet's plural wives, despite intense research by multiple investigators.
Polygamous husbands living when polygamy is illegal face unique challenges as they try to father children with their plural wives. A point arrives when adding new plural wives does not necessarily equate to more sexual relations because the limiting factor is the man’s ability to safely schedule an intimate rendezvous. Whether the man has eight or eighty wives, if external constraints prevent opportunities for secret meetings, sexual encounters will be limited. If such dynamics were present in the Prophet’s complicated life, then additional sealings would have brought minimal increases in his sexual opportunities.
It appears that reliable firsthand accounts in four cases and credible secondhand accounts in another five relationships are available. Thus, evidence for probable sexual relations is identified in nine plural marriages.
(Click on name for link to evidence.)
Historical data supporting the presence of sexual involvement between Joseph Smith and five other plural wives exists, but the evidence suffers from ambiguities or other problems.
Evidence regarding any possible physical relationship between Joseph Smith and his other plural wives is lacking.
 Emily Dow Partridge Young, “Incidents in the early life of Emily Dow partridge,” MS d 2845, fd 1, typescript in possession of the author, page 5; also in Marriott Library, Special Collections. See also Emily D. P. Young, autobiographical sketch, “Written Especially for My Children, January 7, 1877,” manuscript owned by Emily Young Knopp, copy of typescript in possession of the author.
 Oliver Preston Robinson ed., History of Joseph Lee Robinson, History Comes Home, 2007, 54.
 Mary Elizabeth Rollins Lightner, “Remarks” at Brigham Young University, April 14. 1905, vault MSS 363, fd 6, Harold B. Lee Library, Special Collections, 5. Mary Ann Barzee Boice stated in her “History,” that “some” of Joseph Smith’s plural wives “had children.” (Quoted in D. Michael Quinn Papers—Addition—Uncat WA MS 244 [Accession:19990209-c] bx 1.)
 J. D. Stead, Doctrines and Dogmas of Brighamism Exposed, Lamoni, Iowa: RLDS Church, 1911, 218.
 See affidavit of Josephine R. Fisher, February 24, 1915, CHL, Ms 3423, folder 1, images 48-49; see also Danel Bachman, "A Study of the Mormon Practice of Plural Marriage Before the Death of Joseph Smith." M.A. thesis, Purdue University, 1975, 141. See discussion in Richard S. Van Wagoner observed: “Mormon Polyandry in Nauvoo,” Dialogue, 18 (Fall 1985) 3: 78fn12.
 Joseph E. Robinson, Diary, Entry for October 26, 1902, MS 7866, LDS Archives. Olive Frost died October 6, 1845.
 Alvin Smith (June 15, 1828 – June 15, 1828); twins Thaddeus Smith (April 30, 1831 – April 30, 1831) and Louisa Smith (April 30, 1831 – April 30, 1831); Joseph Smith III (November 6, 1832 – December 10, 1914); Frederick Granger Williams Smith (June 29, 1836 – April 13, 1862); Alexander Hale Smith (June 2, 1838 – August 12, 1909); Don Carlos Smith (1840 Died at 14 months); David Hyrum Smith (November 17, 1844 – August 29, 1904). A misreading of Joseph Smith's journal for December 26, 1842 has resulted in the supposition that Emma suffered a miscarriage that day. The History of the Church records: "I found my wife Emma sick. She was delivered of a son, which did not survive its birth." (5:209.) Further scrutiny of the original text indicates a more correct transcription should read: "Sister Emma sick, had another chill." (Scott H. Faulring, ed. An American Prophet’s Record: The Diaries and Journals of Joseph Smith. Salt Lake City: Signature Books, 1989, 258.)
 See Joseph F. Smith, Affidavits folders 1 and 2, Ms 3423 and affidavit books 1-4, CHL;  “Our Own Correspondent,” “The Mormon Church War,” Daily Evening Bulletin, San Francisco, September 1, 1869.
 Angus Munn Cannon, “Statement of an interview with Joseph Smith, III, 1905,” regarding conversation on October 12, 1905, MS 3166, CHL.
 Allegations that Joseph Smith was involved with either some form of birth control or abortions have been made. See Fawn M. Brodie, No Man Knows My History: The Life of Joseph Smith, the Mormon Prophet, 2nd rev. ed. New York, 1971, 346 and W. Wyl, pseud. [Wilhelm Ritter von Wymetal]. Mormon Portraits, or the Truth About Mormon Leaders From 1830 to 1886. Salt Lake City: Tribune Printing and Publishing Co., 1886, 59. However, no evidence has been found to support these accusations. Neither did Brodie or Wyl present any credible documentation.