While the debate over illegal immigration tends to focus on how to control and treat those who make it across our nation’s borders, a more enduring challenge for the U.S. government has been what to do to stop legal entrants from overstaying their allotted time here.

The problem of so-called visa “overstays”—which make up about 40 percent of the 11 million people living illegally in the U.S.—will continue on past the Obama administration and follow the next president.