Both the General Assembly and the Security Council consider disarmament topics, in accordance with Articles 11, 26 and 47 of the UN Charter.
They have also created subsidiary bodies that focus on disarmament matters.
The UN Office for Disarmament Affairs (UNODA) provides support to the disarmament bodies and promotes disarmament efforts.
The Security Council has established the UN Security Council Committee Established pursuant to Resolution 1540 (2004) concerning the proliferation of Weapons of Mass Destruction. Other subsidiaries of the Security Council may also consider disarmament matters, in particular the sanctions committees.
The General Assembly considers disarmament and has created several subsidiaries that deal with the topic.
UN General Assembly First Committee is the main committee of the General Assembly dedicated to disarmament.
The General Assembly has held 3 special sessions on disarmament, and called for a 4th.
The first special session on disarmament established four bodies (A/RES/S-10/2) :
The General Assembly has held three special sessions on the question of disarmament; a fourth has been called for by multiple General Assembly resolutions.
The UN Office for Disarmament Affairs (UNODA) provides support to the disarmament bodies created by the General Assembly and the Security Council and generally promotes disarmament efforts.
UNODA was established by General Assembly resolution 61/257 of 15 March 2007, as a successor to the Department for Disarmament Affairs (DDA).
A complete history can be found in Chapter 4 of The United Nations and nuclear orders (link to ebook for UNHQ)
UNODA has published The United Nations Disarmament Yearbook since 1946