How has the modern presidency acquired legislative powers?

Your question hits on a fascinating and controversial topic—the increasing use of executive power in the modern presidency. In the constitution of the United States, the legislative branch, generally speaking, is tasked with the creation of law, while the presidency, also called the executive branch, is tasked with enforcing law. Similarly, the legislative branch has the responsibility of declaring war on foreign powers and ratifying treaties, while the president has the power of Commander in Chief over the armed forces.

In modern presidencies (and perhaps even before!), these distinctions have begun to blur. President Obama, for example, has taken executive action on the highly charged topics of gun control and immigration, and his critics describe these actions as an overreach of presidential power into the domain of the legislative branch.

Similarly, since World War II, more power in foreign affairs has flowed to the presidency. The Korean War and the first Gulf War were not formally declared by Congress, but were rather authorized by UN Security Council resolutions and pursued by the executive branch, with funding from Congress, but not a formal declaration of war. Modern presidents have similarly pursued executive agreements in diplomacy rather than formal treaties; while formal treaties must be ratified by the Senate, executive agreements can be made with only the power of the presidency. The Iran nuclear deal, negotiated by President Obama and Secretary Kerry, is one such example of an executive agreement.