Redeploying U.S. Nuclear Weapons to South Korea: Background and Implications in Brief [September 14, 2017] [open pdf - 560KB]
"The United States deployed nuclear weapons on the Korean Peninsula between 1958 and 1991. Most of these weapons were intended to deter a ground invasion from North Korea by providing capabilities needed to slow or stop advancing troops and by convincing North Korea that any attack would invite unacceptable damage on the North in retaliation. Their presence was also meant to reassure South Korea of the U.S. commitment to South Korea's defense. The United States removed these weapons as a part of a broader change in the U.S. nuclear force posture at the end of the Cold War, but it remains committed to defending South Korea under the 1953 Mutual Defense Treaty and to employing nuclear weapons, if necessary, in that defense."
CRS Report for Congress, R44950
Federation of American Scientists: http://www.fas.org/sgp/crs/index.html