Short answers, pulled from the story.
The Non-Proliferation Treaty (NPT) is an international agreement opened for signature in 1968 and in force since 1970. Its objectives are to prevent the spread of nuclear weapons and weapons technology, to promote cooperation in the peaceful uses of nuclear energy, and to advance the goal of nuclear disarmament. As of August 2016, 191 states have become parties to the treaty.
The NPT recognizes five nuclear-weapon states: the United States, which first tested in 1945; Russia (then the Soviet Union), in 1949; the United Kingdom, in 1952; France, in 1960; and China, in 1964. These are the states that built and tested a nuclear explosive device before the 1st of January 1967, the treaty's cutoff date.
Four states have never signed the NPT: India, Pakistan, Israel, and South Sudan. India and Pakistan have openly tested and declared nuclear weapons, Israel maintains a policy of deliberate ambiguity about its nuclear status, and South Sudan has not joined since becoming independent in 2011.
North Korea's withdrawal from the NPT became effective on the 10th of April 2003, making it the only state ever to leave the treaty. It cited the United States' policy toward the DPRK as the reason, and conducted its first nuclear test on the 9th of October 2006. North Korea had originally joined the treaty on the 12th of December 1985 but was found in repeated non-compliance with its IAEA safeguards agreement.
South Africa is the only country to have developed nuclear weapons entirely by itself and then voluntarily dismantled them. South African Ambassador Harry Schwarz signed the NPT in 1991, and by 1994 the IAEA had completed verification and declared that South Africa had fully dismantled its nuclear weapons program.
Article VI requires all NPT parties to pursue negotiations in good faith on effective measures relating to cessation of the nuclear arms race, nuclear disarmament, and general and complete disarmament. The International Court of Justice, in its advisory opinion of the 8th of July 1996, interpreted Article VI as creating an obligation to bring such negotiations to a conclusion, not merely to hold talks indefinitely.