Nuclear disarmament has been a parallel process to nuclear non-proliferation. The nuclear-weapon states have promised to work toward disarmament. In exchange for eventual nuclear disarmament, other states have promised not to develop nuclear weaponry.
Nuclear disarmament is an excellent goal. Although verification is a continuing challenge, the requirements of safety and security are good counterbalances, making complete secrecy difficult to achieve. There's always danger of serious accident, and improper handling will one day perhaps lead to major disaster.
The International Atomic Energy Agency (IAEA) and the United Nations Office for Disarmament Affairs have been key focal points for progress with nuclear disarmament and nuclear non-proliferation. But the few states with nuclear weapons have failed to follow-through with their obligations.
The Treaty on the Non-Proliferation of Nuclear Weapons (NPT - link) is seriously belittled by intransigent states not taking nuclear disarmament seriously. A number of the smaller nations have also failed to wholly condemn this lack of progress toward nuclear disarmament -- can we thus label them lackey states? It seems Sweden has become one such state, lacking the courage to consistently support a nuclear weapon-free world...
Link: Foreign Minister Carl Bildt defends Sweden's strategy (P1 radio)