The Limited Test Ban Treaty (LTBT) bans nuclear tests in the atmosphere, outer space and under water. It does not ban tests underground, but does prohibit explosions in the environment if the explosions create debris outside the territory of the responsible state. The biggest issue of the treaty was verification of compliance and agreeing to establish inspections systems. The Soviet Union proposed an international control system but the United States was suspicious of uncontrolled and clandestine efforts. In 1988, it was proposed that the LTBT be extended to all environments, making it a comprehensive test ban, but the United States stood in strong opposition to any amendment that made the Treaty comprehensive.
Opened for Signature: 5 August 1963
Entry into force: 10 October 1963
Official Text: http://www.state.gov/t/isn/4797.htm#treaty
Status and Signatories: http://www.state.gov/t/isn/4797.htm#signatory
ACA Backgrounder: https://www.armscontrol.org/factsheets/Nuclear-Testing-and-Comprehensive-Test-Ban-Treaty-CTBT-Timeline