President Trump’s decision this month to send National Guard troops to Los Angeles against the wishes of Gov. Gavin Newsom has sparked a legal battle that could reshape how much latitude a president has to deploy the military on U.S. soil.

On June 10, days after Mr. Trump federalized the California National Guard in response to protests over immigration raids, the state filed a lawsuit calling the move illegal.

Even as the Trump administration added active-duty Marines to the mix, a judge ordered it to return the National Guard to the control of Mr. Newsom. But an appeals court blocked that move, and Mr. Trump maintains authority over those troops today.

Mr. Trump’s decision to deploy troops came after Immigration and Customs Enforcement started carrying out raids at workplaces in the city, sweeping up hundreds of migrants for potential deportation and drawing protesters. While the majority protested peacefully, a subset committed violent acts like throwing objects and burning vehicles.

Here’s where things stand in the case.

What made Trump’s decision to deploy troops significant?

Normally, governors control their state’s National Guard and dispatch such troops themselves when there is a need to quell civil disorder or fight a natural disaster. On rare occasions, the president may take control of a guard or otherwise deploy troops under federal control on domestic soil, but in recent decades that has happened only at a governor’s request.

Mr. Trump’s move was the first time in more than six decades that a president had taken control of a state guard over a governor’s objections, raising profound questions about presidential power, state sovereignty and civil liberties.