Historically the controversy over the war power and the controversy over the treaty power seem to have been the most important constitutional issues in the scope of the President's foreign affairs power.
Moore, John N.
"The National Executive and the Use of the Armed Forces Abroad,"
Naval War College Review: Vol. 22
, Article 6.
Available at: http://digital-commons.usnwc.edu/nwc-review/vol22/iss1/6