The answer depends on which expert or lawmaker you ask.
By and large, it is understood that a president can respond militarily to a crisis -- at first, in a limited way -- without approval from the legislative branch. Still, some scholars, and plenty of lawmakers, believe that only applies if the U.S. itself is attacked.
Thursday evening, several lawmakers said they did not think President Trump needed approval for this type of limited military action.
Still, most lawmakers believe that any continued involvement in Syria would need to be legally justified either under the current 2001 Authorization for the Military Force or a new AUMF from Congress. The 2001 AUMF passed in both houses after the attacks on September 11, 2001 and gave the go-ahead for military involvement in Afghanistan.
The language of the 2001 AUMF authorized "force against those nations, organizations, or persons" that "planned, authorized, committed, or aided the terrorist attacks that occurred on September 11, 2001, or harbored such organizations or persons."
An AUMF is typically used for a protracted military campaign. For years, some lawmakers and even military officials have argued that the 2001 AUMF is outdated and could not or should not be stretched to cover any further campaigns.
Voting on a new AUMF could be a hard political sell. In 2011, President Obama did not receive a new AUMF for military action against Libya.
Thursday night, some lawmakers called for the House to come back into session to debate the merits of a new AUMF.
Others in the senate questioned whether the Trump administration had acted within its authority.
Talks are ongoing in the senate about the possibility of a new AUMF. In 2013, Obama punted on acting unilaterally and asked Congress to approve any military action in Syria. With both parties divided, it did not pass.
At the time, Trump tweeted that Obama's move to ask for congressional approval was necessary.