Brennan Center for Justice has prepared this martial law explainer. Excerpt:
There are no existing federal statutes that authorize the president to declare martial law. However, while Congress has passed a multitude of laws related to domestic military deployment, these laws do not only create restrictions. Congress has also given the president considerable authority to use troops domestically in ways short of martial law. The Insurrection Act, and potentially Title 32 as well, allow the president to deploy the military to assist civilian authorities with law enforcement activities virtually whenever and wherever the president chooses. In some scenarios, a deployment of troops under these statutes might appear similar to a declaration of martial law. These ambiguities and the breadth of the president’s statutory authority point to the need for Congress to pass legislation that better defines the scope and limits of presidential powers — both for martial law and for other domestic uses of the military.The Brennan Center's full report can be found here.