The idea of reparations—real compensation made to the descendants of slaves or the victims of legalized discrimination—has gained traction since the publication, in 2014, of Ta-Nehisi Coates’s influential article “The Case for Reparations,” which appeared in The Atlantic. But even among proponents of the concept, the ideas about what reparations would mean vary wildly. Questions linger about the intended recipients. Should only descendants of people enslaved on American soil (rather than the Caribbean or elsewhere in the diaspora) be eligible? That is the contention of people using the hashtag ADOS, or American Descendants of Slavery, which has become controversial. How important is genealogical proof to making a claim, given that slavery often did not leave good records? What about Americans who may have had an enslaved ancestor, but have not personally identified as African-American?

Alondra Nelson, a professor of sociology at Columbia University and president of the Social Science Research Council, talked with two prominent scholars who have addressed the issue: Darrick Hamilton, the executive director of the Kirwan Institute for the Study of Race and Ethnicity at Ohio State University, and William A. Darity, the Samuel DuBois Cook Professor of Public Policy at Duke University’s Sanford School of Public Policy. Then Nelson sat down with The New Yorker’s Joshua Rothman to explain the challenges faced.