In a statement Friday, Moore, 70, denied the allegations outlined in a Washington Post story Thursday, stating: "I have never engaged in sexual misconduct."
Moore, 70, has a long history of making outrageous statements.
Here is a review of five hot-button topics the former state judge has weighed in on.
On raceMoore caused controversy after he appeared to refer to Native Americans and Asians as "reds" and "yellows" in a campaign speech, later tweeting similar language.
In his speech, Moore referenced the U.S. Civil War while lamenting the current divisions within the country.
"We were torn apart in the Civil War - brother against brother, North against South, party against party. What changed?" Moore said. "Now we have blacks and whites fighting, reds and yellows fighting, Democrats and Republicans fighting, men and women fighting."
"What's going to unite us? What's going to bring us back together? A president? A Congress?" Roy asked, and then answered, "No. It's going to be God."
The following day, he tweeted similar sentiments, writing in two tweets: "Red, yellow, black and white they are precious in His sight. Jesus loves the little children of the world. This is the Gospel. If we take it seriously, America can once again be united as one nation under God."
Some suggested Moore's tweets indicate he was quoting the children's Bible song, "Jesus Loves the Little Children," by C. Herbert Woolston and George F. Root. Lyrics to that song include the verses: "Jesus loves the little children/all the children of the world/red, brown, yellow, black and white/they are precious in his sight."
On his fellow RepublicansApparently, Moore wasn't looking for friends in the Republican establishment during his primary campaign.
Moore has released advertisements highly critical of Republicans in Washington including Senate Majority Leader Mitch McConnell, R-Ky., Jeff Flake, R-Ariz., and Lindsey Graham, R-S.C., and Speaker of the House Paul Ryan, R-Wis.
"Send them all a message," one ad says, calling out the Senate majority leader's "D.C. slime machine."
On Sharia lawDuring an interview with Vox in September, Moore was asked if he believes Sharia law is a danger to America.
"There are communities under Sharia law right now in our country. Up in Illinois. Christian communities; I don't know if they may be Muslim communities," Moore told Vox.
When asked by Vox which communities he was specifically referring to, he did not provide more details.
"Well, there's Sharia law, as I understand it, in Illinois, Indiana - up there. I don't know," Moore said.
Further pressed, Moore said: "Well, let me just put it this way - if they are, they are; if they're not, they're not. That doesn't matter. Oklahoma tried passing a law restricting Sharia law, and it failed. Do you know about that?"
On the Sept. 11 terrorist attacksMoore allegedly made comments about the Sept. 11, 2001 terrorist attacks during a February campaign stop, according to a video reviewed by CNN.
"'Because you have despised His word and trust in perverseness and oppression, and say thereon ... therefore this iniquity will be to you as a breach ready to fall, swell out in a high wall, whose breaking cometh suddenly at an instance,'" Moore said, quoting a passage in the Old Testament's Book of Isaiah, according to CNN. He then added: "Sounds a little bit like the Pentagon, whose breaking came suddenly, at an instance, doesn't it?"
Later in the video, CNN reports that Moore suggested that God was mad at the United States because "we legitimize sodomy" and "legitimize abortion."
On gay rightsMoore has been outspoken in his opposition to homosexuality for many years.
In 2005, Moore said, "Homosexual conduct should be illegal," according to a CSPAN2 video discovered by CNN in September before the state's Republican primary.
Three years before that interview took place, when Moore was serving as the chief justice of Alabama's Supreme Court, he used a child's mother's sexual orientation as a reason to rule in favor of the child's father in a custody dispute, according to court documents.
"Homosexual behavior is a ground for divorce, an act of sexual misconduct punishable as a crime in Alabama, a crime against nature, an inherent evil, and an act so heinous that it defies one's ability to describe it," the court's decision, ordered under Moore, reads. "That is enough under the law to allow a court to consider such activity harmful to a child."