United States presidents issue executive orders to help officers and agencies of the executive branch manage the operations within the federal government itself.
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Executive orders have the full force of law when they take authority from a legislative power which grants its power directly to the Executive by the Constitution, or are made pursuant to Acts of Congress that explicitly delegate to the President some degree of discretionary power.
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Like both legislative statutes and regulations promulgated by government agencies, executive orders are subject to judicial review, and may be struck down if deemed by the courts to be unsupported by statute or the Constitution.
Major policy initiatives require approval by the legislative branch, but executive orders have significant influence over the internal affairs of government, deciding how and to what degree legislation will be enforced, dealing with emergencies, waging wars, and in general fine-tuning policy choices in the implementation of broad statutes.