Conqueror is[update] the only nuclear-powered submarine to have engaged an enemy ship with torpedoes, sinking the cruiser General Belgrano during the 1982 Falklands War.

Conqueror arrived in the exclusion zone around the Falkland Islands 21 days later and was ordered to scan the area for Argentine shipping, particularly the aircraft carrier Veinticinco de Mayo ("25th of May").

By the early 1980s the ARA were no longer receiving parts from the USA to maintain these systems, but the destroyers had recently been re-armed with French Exocet anti-ship missiles.

In the intervening period, General Belgrano had retired from her attack position and turned west, since Veinticinco de Mayo was not yet ready to engage the British fleet.

General Belgrano was unable to issue a Mayday signal because of electrical failure; this and poor visibility meant the two escorting destroyers were unaware of the sinking until some hours later.

Conqueror did not fire again for the remainder of the war, but helped the task force by using sophisticated monitoring equipment to track Argentine aircraft departing from the mainland.

After the war, Conqueror returned to Faslane, flying a Jolly Roger, a customary act of Royal Navy submarines after a kill.

[15] On 2 July 1988 Conqueror was involved in a collision with the Army Sail Training Association yacht Dalriada south of the Mull of Kintyre.