So-called sanctuary laws enacted in hundreds of places across the United States, from big cities like Philadelphia and Chicago to rural counties in Nebraska and New Mexico, have become targets in the nation’s divisive immigration debate.

Democrats have long championed the laws, which limit cooperation with federal immigration authorities, as a way to create safe and welcoming environments for undocumented immigrants. President-elect Donald J. Trump and Republicans say they fuel crime and make cities unsafe.

Now, as Mr. Trump prepares to re-enter the White House, the future of the sanctuary movement is likely to take center stage, most notably in New York, a city that is home to more than 400,000 undocumented immigrants and has long cherished its reputation as a safe haven.

Mayor Eric Adams, a Democrat, is intent on changing the city’s sanctuary laws to allow his administration to work more closely with federal agents to deport criminals. But even as New Yorkers have signaled a greater appetite for a harder line on immigration as the city navigates a two-year migrant influx, many Democrats still oppose Mr. Adams’s stance.

As changes loom, here’s what you need to know about New York’s sanctuary laws.

How did New York become a sanctuary city?

The term “sanctuary city” is not a legal designation, but rather a catchall phrase to describe jurisdictions like New York that have adopted policies that afford some protection to undocumented immigrants against federal agents seeking to detain or deport them.

Sanctuary policies often vary, but think of them as a wall blocking communication between immigration agents and city workers who interact with undocumented immigrants. They were initially enacted to encourage immigrants to report crimes, get medical treatment, enroll in schools and seek other city services without fear that they would be detained.