James Cook's third and final voyage (12 July 1776 4 October 1780) took the route from Plymouth via Cape Town and Tenerife to New Zealand and the Hawaiian Islands, and along the North American coast to the Bering Strait.

Its ostensible purpose was to return Omai, a young man from Raiatea, to his homeland, but the Admiralty used this as a cover for their plan to send Cook on a voyage to discover the Northwest Passage. HMS Resolution, to be commanded by Cook, and HMS Discovery, commanded by Charles Clerke, were prepared for the voyage which started from Plymouth in 1776.

Omai was returned to his homeland and the ships sailed onwards, encountering the Hawaiian Archipelago, before reaching the Pacific coast of North America. The two charted the west coast of the continent and passed through the Bering Strait when they were stopped by ice from sailing either east or west. The vessels returned to the Pacific and called briefly at the Aleutians before retiring towards Hawaii for the winter.

At Kealakekua Bay, a number of quarrels broke out between the Europeans and Hawaiians culminating in Cook's death in a violent exchange on 14 February 1779. The command of the expedition was assumed by Charles Clerke who tried in vain to find the passage before his own death. Under the command of John Gore the crews returned to a subdued welcome in London in October 1780.

James Cook (7 November 1728 – 14 February 1779) was a British explorer, navigator, cartographer, and captain in the British Royal Navy, famous for his three voyages between 1768 and 1779 in the Pacific Ocean and to Australia in particular. He made detailed maps of Newfoundland prior to making three voyages to the Pacific, during which he achieved the first recorded European contact with the eastern coastline of Australia and the Hawaiian Islands, and the first recorded circumnavigation of New Zealand.

Cook joined the British merchant navy as a teenager and joined the Royal Navy in 1755. He saw action in the Seven Years' War and subsequently surveyed and mapped much of the entrance to the St. Lawrence River during the siege of Quebec, which brought him to the attention of the Admiralty and the Royal Society. This acclaim came at a crucial moment for the direction of British overseas exploration, and it led to his commission in 1766 as commander of HMS Endeavour for the first of three Pacific voyages.

In these voyages, Cook sailed thousands of miles across largely uncharted areas of the globe. He mapped lands from New Zealand to Hawaii in the Pacific Ocean in greater detail and on a scale not previously charted by Western explorers. He surveyed and named features, and recorded islands and coastlines on European maps for the first time. He displayed a combination of seamanship, superior surveying and cartographic skills, physical courage, and an ability to lead men in adverse conditions.

Cook was attacked and killed in 1779 during his third exploratory voyage in the Pacific while attempting to kidnap the ruling chief of the island of Hawaiʻi, Kalaniʻōpuʻu, to reclaim a cutter taken from one of his ships after his crew took wood from a burial ground. He left a legacy of scientific and geographical knowledge that influenced his successors well into the 20th century, and numerous memorials worldwide have been dedicated to him.