[1] After graduating from Granite High School in 1944 at the height of World War II, Maxwell enlisted in the United States Army.

While pursuing an undergraduate education at the University of Utah before leaving on his mission, Maxwell met Colleen Hinckley (1928–2016).

After Maxwell returned from his mission, he resumed courting Colleen, and they were married in the Salt Lake Temple on November 22, 1950.

In 1961, he was secretary to the Board of Trustees, followed by dean of students in 1962, and later vice president for planning and public affairs.

Maxwell began serving as an LDS general authority in 1974, when he was called as an Assistant to the Quorum of the Twelve Apostles.

Maxwell was ordained an apostle by N. Eldon Tanner on July 23, 1981, after Gordon B. Hinckley became a counselor in the First Presidency.

Maxwell wrote approximately 30 books concerning religion and authored numerous articles on politics and government for local, professional and national publications.

[5] Commenting on his speaking and writing styles at Maxwell's funeral, church president Gordon B. Hinckley said, I know of no other man who spoke in such an interesting and distinct manner.

He was a perfectionist determined to exact from every phrase and sentence vivid imagery that brought the gospel to life.

An estimated 4,000 people attended the funeral in the Tabernacle or via video in the Salt Lake Assembly Hall or the Joseph Smith Memorial Building.