Simpson has been a strong critic of the U.S. Supreme Court ruling Citizens United v. FEC, calling for the 28th Amendment to the U.S. Constitution to overturn the Supreme Court's decision in that case. In an interview with Wyoming Public Radio, Simpson said: "I think most Americans would like to see reasonable limits on campaign spending."

Alan Simpson graduated from Cody High School in Cody, Wyoming, in 1949, and attended Cranbrook School in Bloomfield Hills, Michigan, in 1950 for a postgraduate year. He graduated in 1954 from the University of Wyoming with a Bachelor of Science degree, and in 1958 with a Juris Doctor. Like his brother, he was a member of the Alpha Tau Omega fraternity at the University of Wyoming.

In 1954 he married the former Susan Ann Schroll, who was a fellow UW student from Greybull, Wyoming. He served in the United States Army in Germany from 1955 to 1956, with the 10th Infantry Regiment, Fifth Infantry Division, and with the 12th Armored Infantry Battalion, Second Armored Division.

Born in Denver, Colorado, Simpson graduated from the University of Wyoming's law school (1958). Simpson served in the Wyoming House of Representatives (1965-77) and won election to the United States Senate (1978). His father, Milward Simpson, had served in the same seat (1962-67). Simpson served as the Senate Republican Whip (1985-95). After serving three terms in the Senate, Simpson declined to seek re-election in 1996.

Simpson served from 1965 to 1977 in the Wyoming House of Representatives from Park County, but he had already left the chamber four years before his brother entered it for a four-year stint.

Simpson was elected to the U.S. Senate on November 7, 1978, but was appointed to the post early on January 1, 1979, following the resignation of Clifford P. Hansen. From 1985 to 1995, Simpson was the Republican whip, Assistant Republican Leader in the Senate, having served with then Republican Leader Bob Dole of Kansas. He was chairman of the Veterans' Affairs Committee from 1981 to 1985 and again from 1995 to 1997 when Republicans regained control of the Senate. He also chaired the Immigration and Refugee Subcommittee of Judiciary; the Nuclear Regulation Subcommittee; the Social Security Subcommittee and the Committee on Aging. He was a moderate conservative. He supported abortion right and voted against ban of late term abortion which did not include the exception of physical health(includes only life threatening exception)in 1995 and 1996. However he opposed federal funding for abortions and supported Hyde-Amendment. He was also the co-sponsor of immigration bill regulating more immigration.

Simpson has an older brother, Peter K. Simpson of Cody, a Historian and a former administrator at the University of Wyoming in Laramie, who served in the Wyoming House of Representatives from 1981 to 1984, having represented Sheridan County, while he was then an administrator at Sheridan College. Pete Simpson was the 1986 Republican gubernatorial nominee, having sought the office while his younger brother was serving in the U.S. Senate.

Simpson teaches periodically at his alma mater, the University of Wyoming at Laramie, with his brother Pete. He has completed serving as chairman of the UW capital "Campaign for Distinction," which raised $204 million. That success was celebrated by the gala event, "An Extraordinary Evening", featuring former President George H.W. Bush (who had reportedly considered Simpson for the vice presidency in 1988) and Vice President Dick Cheney, another UW alumnus, and his wife Lynne V. Cheney.

Simpson also played himself in a cameo appearance for the 1993 film Dave.

The June 7, 1994, edition of the now-defunct supermarket tabloid Weekly World News reported that 12 U.S. senators were aliens from other planets, including Simpson. The Associated Press ran a follow-up piece which confirmed the tongue-in-cheek participation of Senate offices in the story. Then-Senator Simpson's spokesman Charles Pelkey, when asked about Simpson's galactic origins, told the AP: "We've got only one thing to say: Klaatu barada nikto". This was a quotation from a classic science fiction film, The Day the Earth Stood Still (1951), in which an alien arrives by flying saucer in Washington, D.C.

In 1995, he lost the whip's job to Trent Lott of Mississippi, and he did not seek reelection to the Senate in 1996. From 1997 to 2000, Simpson taught at the Joan Shorenstein Center on the Press, Politics, and Public Policy at Harvard University's John F. Kennedy School of Government in Cambridge, Massachusetts, and he served for two years as the Director of the Institute of Politics at the Kennedy School.

In 2001, Simpson became Honorary Chairman of the Republican Unity Coalition (RUC), a gay/straight alliance within the Republican Party. In that capacity, Simpson personally recruited former President Gerald R. Ford, Jr., to serve on the RUC advisory board.

In 2002, Simpson was involved in the Republican gubernatorial primary on behalf of former Democrat Eli Bebout of Riverton. Simpson criticized Bebout's principal challengers Raymond Breedlove Hunkins of Wheatland, and Bill Sniffen of Lander in Fremont County. Bebout defeated the two but then lost the general election to the Democratic nominee Dave Freudenthal, a former United States Attorney appointed by U.S. President Bill Clinton.

In 2006, Simpson was one of ten-member (five Democratic and five Republican) contributors to the Iraq Study Group Report.

Simpson then returned to his home of Cody and practices law there with his two Lawyer sons (William and Colin) in the firm of Simpson, Kepler and Edwards. The three are also partners in the firm of Burg Simpson Eldredge Hersh and Jardine of Englewood, Colorado. Colin M. Simpson, the third generation of his family in Wyoming politics, was a Republican member of the Wyoming House of Representatives who served as Speaker of the House for the 59th session of the Legislature, 2008 to March 2010. He was a candidate for governor, having finished fourth in the primary in 2010.

Simpson was appointed in 2010 to co-chair President Obama's National Commission on Fiscal Responsibility and Reform with co-chair Erskine Bowles.

Simpson is on the Board of Directors at the National Institute for Civil Discourse (NICD). The institute was created at the University of Arizona after the tragic shooting of former Congresswoman Gabrielle Giffords in 2011, that killed 6 people and wounded 13 others.

In December 2012, Simpson filmed a Gangnam Style video for a campaign, with a man in a tin can costume. The video, aimed at young people, is called "The Can Kicks Back," a reference to the tendencies of members of Congress to forever "kick the can down the road" in order to avoid making difficult decisions about lowering the nation's ballooning debt. In the video, Simpson admonishes younger Americans to make better use of their social media than "instagramming your breakfast and tweeting your first-world problems." He advises younger people to use their considerable social media skills and resources to rally their friends to join The Can Kicks Back. If younger Americans do not take heed, Simpson says, "These old coots will clean out the Treasury before you get there."

In 2016, he joined the Advisory Board of American Promise, a national, cross-partisan, organization that advocates for the 28th Amendment.

On Dec. 4, 2017, The Daily Beast published an article about sexual harassment allegations during the 1991 Clarence Thomas hearings. Despite the current nationwide reckoning with the Problem of sexual harassment, Simpson repeated the skepticism about Hill's testimony that he exhibited during the original case. He is quoted as saying, "whatever happened to Professor [Anita] Hill, I don’t believe was sexual harassment...I had a wife and mother, and a daughter, who had been through far worse.”