Since taking office, President Trump has relied on the National Guard to help implement a sweeping agenda on crime and immigration, kicking off a blitz of deployments that have rattled cities, tested the limits of his legal authority, and drawn in the Supreme Court.

So far, Mr. Trump has called upon the military force to help stop illegal crossings at the southern border and staff immigration facilities; to guard federal property and personnel amid protests in Chicago, Los Angeles and Portland, Ore.; and to back crime-fighting efforts in Washington, D.C., and Memphis. He has done all this while publicly mulling similar actions in cities like Baltimore, New Orleans and San Francisco.

National Guard deployments to U.S. cities

Who is in charge of National Guard deployments?

The deployments, which have provoked fierce lawsuits from state and local leaders, are not all on the same legal footing. The main difference, according to experts in armed forces law, comes down to who commands the Guard: the president, or the governor of an individual state.

When called into action by a governor responding to a state-level emergency, the Guard serves under a status known as state active duty, under which there is no general prohibition against troops conducting law enforcement. In recent years, Guard members under that status have policed the southern border, patrolled New York City’s subway platforms and helped support crime-fighting efforts in Albuquerque.

But when deployed under the president’s command — typically, when called to train or fight overseas — National Guard troops become federalized and are subject to a section of the U.S. Code known as Title 10, the same laws governing other active-duty military branches.

Crucially, troops under that status are forbidden, with narrow exceptions, from performing law enforcement under the Posse Comitatus Act of 1878, which came about after the federal government withdrew troops from the Southern states defeated in the Civil War.

In Chicago, Los Angeles and Portland, where Mr. Trump has deployed the Guard over governors’ objections, he has done so by placing the troops directly under federal control — itself a legally contentious move. As a result, troops’ activities there are largely restricted to guarding federal property.

A third status, known as Title 32, combines aspects of state and federal duty. In that hybrid designation, Guard troops remain under their governor’s command, but the deployment receives federal funding and comes at the request of the president or secretary of defense.

In Memphis, where the governor is commanding the Guard mission at Mr. Trump’s urging, and in Washington, D.C., where the president has authority over the local Guard, troops have deployed under a hybrid status. Guard soldiers in those cities have more openly patrolled the streets, but they have so far steered clear of serving warrants or making arrests.

Military law experts say the distinction between those different deployment statuses is critical not only to what troops can do on the ground but also to how courts will weigh the legal questions posed by Mr. Trump’s rapid assumption of power.

“There is very little case law on all of this,” said Elizabeth Goitein, a senior director at the Brennan Center for Justice at New York University’s law school, “partly because domestic deployment of the military has happened extremely sparingly in our nation’s history.”

What the courts say

In court, the Trump administration has argued that the president has broad authority to federalize the National Guard anywhere in the country, at any time, whenever he feels it is necessary to enforce the law or suppress disorder.

That power, federal lawyers say, extends from an obscure, rarely invoked statute that gives the president authority to federalize the force in times of rebellion, invasion or when the president is otherwise unable to enforce federal law.

But the Trump administration has gone further, arguing that the same statute grants the president a sweeping exemption from the Posse Comitatus Act, the law barring the use of federal soldiers for law enforcement. Presidents typically have had to invoke the Insurrection Act, an extreme step, to claim such an exemption.

Further complicating the issue are Mr. Trump’s moves to deploy the National Guard across state lines, a step usually taken only with the consent of all parties involved, said Mark Nevitt, an associate professor at Emory University School of Law.

Mr. Trump has pushed to deploy federalized Guard troops from Texas to Chicago, and troops from California to Portland, while several Republican governors have agreed to send troops under their command to Washington, D.C.

State leaders in California, Illinois and Oregon have contested the Trump administration’s arguments in court, and rulings so far have been divided. The administration has recently appealed to the Supreme Court in the Illinois case, setting the stage for a high-stakes decision that could shape how the Guard is used moving forward.

Officials in Tennessee and Washington, D.C., have also challenged the deployments to their cities.

Military law experts described Mr. Trump’s actions as a rarity in U.S. history, highlighting that the president’s aggressive maneuvering of federalized Guard troops comes in the face of protests far more subdued than the kind of mass unrest that has been used to justify their use in the past.

But Kevin Greene, a co-director of the University of Southern Mississippi’s Center for the Study of the National Guard, said it also strikes at a question dating back to the country’s earliest days, and the founders’ skepticism of a standing army on domestic soil.

“The history of the United States is about the pendulum swinging back and forth as it relates to the militia and the National Guard, as to who has authority over it, and who should,” he said.