The Pentagon recently dropped barriers to female service members participating in combat roles, raising questions of whether women should be included in the draft were it to be reinstated.
The issue has split the already fractious GOP field.
At a rally in South Carolina Friday, Texas Sen. Ted Cruz slammed three of his Republican opponents who have backed registering women for the draft.
He charged that they were "so addled by political correctness that they think we should put our little girls on the front line. That's crazy."
When the candidates were asked at Saturday's Republican debate if the Selective Service -- the registry that a military draft would draw from -- should include women, Florida Sen. Marco Rubio, former Florida Gov. Jeb Bush and New Jersey Gov. Chris Christie indicated that they did. Christie has since dropped out.
"I have no problem whatsoever with people of either gender serving in combat so long as the minimum requirements necessary to do the job are not compromised," Rubio said. "Now that that is the case, I do believe Selective Service should be opened up for both men and women."
While Bush said he supported the inclusion of women in the Selective Service, he downplayed the chance that it would lead to women being drafted into combat. "The draft's not going to be re-instituted," he said.
Here's a guide to understanding the contentious issue.
What is the Selective Service?
The Selective Service system maintains contact information for young Americans that would be potentially subject to military conscription.
The first U.S. attempt at conscription, or mandatory military service, took place in 1862 during the height of the Civil War. The draft was then brought back during the two World Wars.
The modern draft system, governed by the Selective Service Act, was passed in 1948 during the Cold War.
The draft proved hugely unpopular during the Vietnam War and was curtailed in 1973 with the end of America's involvement there.
The Selective Service was reinstated in 1980 following the Soviet Union's invasion of Afghanistan.
The stated mission of the Selective Service is to "furnish manpower to the Defense Department during a national emergency." The Pentagon has never called for the draft to be reinstated.
According to the Selective Service website, "Almost all male U.S. citizens and male immigrants, who are 18 through 25, are required to register with Selective Service." Not having registered is illegal and can have adverse effects for people seeking federal employment or student loans.
In 2013, then-Secretary of Defense Chuck Hagel, a Vietnam veteran, said registering for the Selective Service "provides a hedge against a catastrophe we do not yet anticipate," as well as reminds "our youth that public service is a valid part of American Citizenship."
Why aren't women currently required to register?
The Supreme Court in 1981 upheld Congress' decision to exempt women from registering for the Selective Service, ruling that since women were restricted from combat, they would not be needed in the event of a draft.
"The existence of combat restrictions clearly indicates the basis for Congress' decision to exempt women from registration," Justice William Rehnquist wrote at the time.
According to the Selective Service system's website, the law "refers specifically to 'male persons' in stating who must register and who would be drafted," therefore women are not required to register.
The Service also says that Congress would have to amend the law in order for women to be drafted into the military.
What does the military say about including women in the draft?
A Pentagon spokesperson, Marine Lt. Col. Gabrielle Hermes, told CNN that Secretary of Defense Ash Carter "believes it stands to reason that Congress should review whether women should register for selective service" now that all combat positions are open to women.
And at the beginning of February, the Commandant of the Marine Corps, Gen. Robert Neller, and the Chief of the Army, Gen. Mark Milley, voiced their support for the inclusion of women in the Selective Service now that all military positions, including combat roles, have been opened to women. The U.S. Marine Corps had opposed the opening of certain combat specializations to women.
Brooke Stedman of the Women in International Security, a non-government organization that aims to advance the leadership and professional development of women in the field of international peace and security, agreed with the generals.
"If we wish to uphold and promote gender equality, then women should also be required to enroll in the Selective Service," she told CNN. "Arguments that the American people don't want to see their daughters and sisters drafted are offensive and ignorant. Are we not equally scared to see our sons and brothers drafted?"
Is the Selective Service worth keeping?
While some are seeking to include women, a bipartisan group is calling for a different approach: abolishing the Selective Service for everyone.
Rep. Mike Coffman, a Colorado Republican, is leading the effort. Coffman himself volunteered for the Army in 1972 during the last days of the draft.
"What I saw then was an army that was broken from Vietnam, full of low morale and discipline problems," Coffman told CNN.
He later left the Army and became a Marine infantry officer, serving in Iraq during the first and second Iraq wars.
He described the all-volunteer force he participated in during those conflicts as having "an enormous increase in capability and quality."
Coffman, a Rubio supporter, argued that requiring only men to register is unconstitutional, but although his legislation has attracted bipartisan co-sponsors, he thinks Congress is unlikely to act unless there is a constitutional challenge in the courts.
Hermes said the secretary believes that "The All-Volunteer Force has served our nation well," adding that "the decision regarding the role of the Selective Service and who should register and participate is a decision that needs to be part of a much broader national discussion."
Coffman called the Selective Service "outdated" and said it costs taxpayers an estimated $23 million a year.
"Young men who don't register for the selective service are still penalized by the U.S. government," he said. "We need to get rid of this mean-spirited and outdated system and trust that if the need should arise, Americans -- both male and female -- will answer the call to defend our nation."