(CNN) Confederate landmarks -- as they originally were intended and in the ways some communities have sought to change them -- reflect the ever-evolving story of America.

South Carolina removed the Confederate flag from statehouse grounds in 2015, after a self-described white supremacist killed nine black churchgoers in Charleston

Since then, a movement to pull Confederate iconography from government and public property has been gathering steam.

The effort pits those who see the symbols as tributes to Southern heritage against others who regard them as a glorification of a sordid history of racism.

Suddenly, a question long debated among historians has become the subject of a national conversation: What should happen to these relics of a bygone era? There's no clear consensus, but most historians agree: It's up to individual communities to make decisions that reflect their values.

Many historians also agree that Confederate monuments shouldn't be destroyed, since they can impart important lessons about the ugliness of the past. That leaves three ways in which cities around the country could deal with them: keep them and add context, move them to museums, or move them elsewhere.

Still, some are finding it hard to locate new homes for these items -- many monolithic in scale -- sometimes because of the history they represent.

Part of Orlando's "Johnny Reb" statue is removed from Eola Park in June.

Keep them and add context

Monuments don't build themselves; as such, they say more about the people who made them than the figures they portray.

Southern heritage groups were responsible for most monuments erected across the country during Reconstruction, the post-Civil War era marked by a backlash to integration that fueled Jim Crow policies of legalized discrimination and led to more than 4,000 lynchings of black people in the Deep South.

During this time, groups such as the United Daughters of the Confederacy and Sons of Confederate Veterans built monuments that promoted the "Lost Cause" ideology -- the belief that states' rights, not slavery, was the Confederacy's principal cause, despite overwhelming evidence to the contrary.

To historians, what tends to be missing from Confederate monuments is the full picture of what they really stand for. Instead of moving them, some academics suggest adding historically accurate context so people can learn from them.

"What we want to do is inject historical perspective and facts into these monuments and encourage people to think of them as pieces of history or artifacts instead of objects of veneration," said Sheffield Hale, president and chief executive officer of the Atlanta History Center

"These objects are inherently problematic, and that's why they're potentially effective teaching tools," Hale said. "They provoke conversation about a period that a lot of people have forgotten about or don't want to talk about."

The equestrian statue of Gen. Robert E. Lee looms over Monument Avenue in Richmond, Virginia.

That's the plan in Richmond, Virginia, the short-lived capital of the Confederate States of America. The city's mayor appointed a commission last week to research ways to add context to Monument Avenue, a boulevard lined with statues of Confederate generals, as well as tennis legend and Richmond native Arthur Ashe.

Critics say contextualization has its challenges. If a statue of Lee dominates a traffic circle, what impact would a small plaque have on motorists flying by?

Finding the right approach is another challenge. It took nearly two years for the University of Mississippi to agree on language for a new plaque for a 1906 statue of a Confederate soldier.

In addition to explaining the "Lost Cause" ideology that the monument's builders subscribed to, the new plaque describes how the statue was a meeting place for a rally opposing school integration in 1962.

"This historic statue is a reminder of the university's divisive past," the plaque reads, in part. "Today, the University of Mississippi draws from that past a continuing commitment to open its hallowed halls to all who seek truth, knowledge, and wisdom."

Relocate them to museums

For some, the problem with contextualization is it keeps monuments in places where they may not be wanted by all.

"To leave them as they are is in many cases a giant middle finger to the communities in which they sit," said Anne Sarah Rubin, a history professor at the University of Maryland, Baltimore County.

Barricades go up as the removal of a Jefferson Davis begins in May in New Orleans.

"Monuments were never fully representative of the localities they were put up in. They were put up to send messages and create false narratives about what the war was about and who should be celebrated," said Rubin, author of "Through the Heart of Dixie: Sherman's March and American Memory."

Moving them to a museum lets people choose whether to interact with them within a proper historical context. Many museums already hold items from dark chapters in history, including racist memorabilia from the Jim Crow era, said University of Pittsburgh assistant professor Keisha N. Blain.

"Unlike public spaces -- like parks -- museums are controlled spaces where experienced staff members can provide historical context for visitors, and people can choose to see the monuments or not," said Blain, co-editor of "The Charleston Syllabus: Readings on Race, Racism, and Racial Violence."

But even if museums want them, it can be hard to make room for six tons of bronze or marble.

A statue of Confederate leader Jefferson Davis is removed in 2015 from University of Texas' South Mall.

It took almost two years for the University of Texas to find a new home for a statue of Jefferson Davis. It ended up back on campus, as a museum exhibit that centers more on the controversy surrounding the statue than the person it portrays.

The removal of four monuments from public spaces in New Orleans stunned historians who thought, after six years of debate, that the day would never come. New Orleans Mayor Mitch Landrieu vowed to move the four statues to a museum, but it remains to be seen where they'll end up.

St. Louis began removing a Confederate monument from a city park Monday, after reaching an agreement with the Missouri Civil War Museum.

The museum, which sued the city over ownership of the statue and its base, will bear the cost of the removal and be responsible for housing the monument until a permanent home is found at another Civil War museum, battlefield or cemetery outside St. Louis County.

A new home has yet to be found for a Confederate monument in St. Louis.

Move them elsewhere

Another natural resting place for ousted monuments has been historic cemeteries, often those with a Civil War connection.

Orlando's "Johnny Reb" statue is destined for the Confederate veterans' section of city-owned Greenwood Cemetery, after it was removed in June from a public park.

The monuments also can be sent back to the heritage groups that made them in the first place. After voting to remove "Old Joe," the city council of Gainesville, Florida, offered it to the local United Daughters of the Confederacy chapter. The group has until mid-July to respond.

"If historic preservationists want to save a house, they raise the money to save the house and move into onto property they own," said Karen Cox, history professor at the University of North Carolina at Charlotte.

"If these groups are so in love with their monuments, they should follow suit -- pay for it to be removed, find piece of property and then worship to their heart's content."