Born March 13, 1811, William B. Smith was one of the younger brothers of the Prophet Joseph Smith. He recalled how the family had been well-respected and relied upon prior to the time that Joseph began telling others about the First Vision. Unlike Joseph, who was generally calm and pleasant, William had a fiery temper, which was often manifest when he was defending the Prophet, the Church, or other family members. His mother, Lucy Mack Smith, recalled one incident when William returned home to find an angry group of men demanding a debt payment from the family. William “seized a large handspike, sprang up stairs, and, in one instant, cleared the scoundrels out of the chamber … exclaiming, ‘Away from here, you cut-throats, instantly, or I will be the death of every one of you.’ 
William was baptized in June of 1830, and left soon thereafter to serve a mission in New York and Pennsylvania. On February 15, 1835, he was called as a member of the Quorum of the Twelve Apostles of The Church of Jesus Christ of Latter-day Saints. He was disfellowshipped on May 4, 1839, then restored to the Quorum of the Twelve on May 25, 1839.
Williams fiery temper often times carried him in a direction opposite the Church and his brother, Joseph. His headstrong attitude and passion either led him as a strong advocate of the Church, or turned him heavily against it. Although he repented of his attacks on Joseph, and was forgiven, his actions were never quite trusted by the main body of the Church. He refused a call to serve with other members of the Twelve in England, and when he was asked to collect funds for the building of the Nauvoo Temple, he kept the funds for himself.
Following the Prophet’s death, William was supportive of the Quorum of the Twelve Apostles and their call to leadership. He was also told by Brigham Young that he had the right to be called as Patriarch of the Church: his father, Joseph Smith, Sr., and then his older brother, Hyrum, had served prior to their deaths. William accepted the call, but was not ordained until May 24, 1845, nearly a year after the death of Hyrum. Unfortunately, William soon began to presume upon his authority by claiming that his position gave him the right to be the next President of the Church.
In October, 1845, William’s apostolic calling was revoked. He was excommunicated soon after and was furious toward the Church and its leaders. He joined briefly with the Strangite group, and also attempted to begin his own church in Kentucky, but never received much of a following. He served as a member of the Union Army during the Civil War (at which time he adopted the middle initial "B"), and when he returned home joined with the Reorganized Church of Jesus Christ of Latter-day Saints that was currently being presided over by his nephew, Joseph Smith III.
William lived longest of all the Smith brothers by nearly 50 years. Samuel Smith followed Joseph and Hyrum in death by just a month on July 30, 1844, after suffering from exposure and fatigue after the martyrdom of his brothers. Don Carlos (d. 1841) and Alvin (d. 1823) both passed away before them. William passed away on November 13, 1893, at the age of 82, in Osterdock, Iowa.
Bibliography: Susan Easton Black, Who’s Who in the Doctrine & Covenants, pp. 300-304.
Additional Resources: "Joseph Smith's Challenging Brother - William B. Smith"
- Lucy Mack Smith, History of Joseph Smith by His Mother, ed. Preston Nibley, pp. 183-184.