Twenty years after his return from the disastrous voyage with HMS Wager, in which the ship was wrecked off the coast of Chile and several of the crew mutinied against the acting captain, David Cheap, John Byron was commissioned by the Royal Navy to lead a secret expedition to establish a permanent British base in the South Atlantic Ocean.

In June 1764, Byron, on board the frigate HMS Dolphin, set sail from Woolwich, accompanied by HMS Tamar, and travelled first to Plymouth, before making stops at Madeira and Rio de Janeiro. Upon leaving Brazil, Byron went in search of Pepys Island; an island spotted almost a century earlier off the coast of South America. The island was not found at its charted location and Byron soon abandoned the search, judging it to have been a phantom discovery. However, shortly afterwards, the expedition did encounter the Falkland Islands, remarking that the harbours there could "receive the whole royal navy of England, which might lie here in the greatest security".

Before passing through the Magellan Strait, the expedition encountered a nomadic community of Indigenous peoples on Tierra del Fuego. The height of these people (probably around six feet) was such a shock to the much shorter sailors that they believed they were the 'giants' previously mentioned by Magellan and other explorers. It was an amiable encounter, and Byron traded with the community for supplies before departing. Once into the Pacific, the expedition made a short stop at the Juan Fernandez Islands, famed for being the home of the castaway Alexander Selkirk (the inspiration for Robinson Crusoe), before sailing west.

After a month without seeing land, the crew, suffering greatly from the effects of scurvy, sighted a small low-lying island. Unfortunately, the atoll they spotted, though abundant with coconuts and other plant-life, was inaccessible for the vessels and the Indigenous population was hostile to their presence. This continued across several other atolls, which Byron named the "Islands of Disappointment". However, shortly afterwards, they were able to make land at three more atolls which Byron named Coral Island, King George Island and Prince of Wales' Island where they were able to resupply with coconuts, fish and fresh water. In July 1765, Byron reached the island of Nikunau (now part of Kiribati) marking the first documented European encounter with the Indigenous population there.

Soon after leaving Nikunau, the expedition spotted familiar islands in the Indonesian archipelago and set forth for the port of Batavia (now Jakarta) where the ships were refitted. On leaving Batavia, Byron sailed for home, reaching the Cape of Good Hope in February and England in May 1766.

Byron's circumnavigation was one of the fastest of the time, completed in less than two years, and HMS Dolphin would achieve the same feat only a few years later under the command of Samuel Wallis, becoming the first ship to twice circumnavigate the globe. This account of the voyage was written by an officer aboard Dolphin and was published in 1767. It records the discoveries made by the expedition and includes some detailed accounts of the wildlife encountered; often remarking on their taste and practical uses to the crew.