Place names tell the story of Long Island in the history of New Netherland. The eastern end of the island--North Fork, South Fork, Southampton, Suffolk--is Old England, while in the west you find names (with an occasional spelling change) that come straight from the Dutch: Nassau, "Heemstede," New Utrecht, and of course "Breuckelen." The island--1,400 square miles of woodland, bay and beach, a rich microcosm of the continent it lay astride---became the principal battleground between the Dutch of New Netherland and the English of New England as they struggled for control of the Eastern Seaboard of North America.
Long before Europeans arrived, the island was carved into loosely structured territories by Indian tribes many of whose names--Montauk, Manhasett, Shinnecock, Patchogue--are still familiar. Most fell into one of two linguistic groups: the Montauk, at the eastern half of the island, and the Delaware, in the west. With Henry Hudson's voyage, the European period, and the Dutch claim, began. In 1611, the Dutch explorer Adriaen Block became the first European to sail into what became known as Long Island Sound. Once he reached its end, he realized the body of land to the east was not a peninsula but an island. The Dutch name--'t Lange Eylandt--was apt, and it stuck.
Technically, Long Island was within the Dutch claim to New Netherland, but from the beginning of the seventeenth century England refused to honor that claim, and preferred to believe that the island fell under the claim of the Plymouth Company charter. But more important than legal claims was the practical matter of settlers. In England, the Civil War was raging in the 1640s, which led to a huge migration of English settlers to the North American colonies. The Netherlands at the same time was experiencing its Golden Age, and comparatively few people were interested in taking up the hard life of a settler. It was thus only a matter of time before English settlers began moving south from the New England colonies, crossed the Sound, and settled on what they considered to be unused, and therefore available, land.
Tensions between the English and Dutch inhabitants of Long Island steadily increased. In 1650, when the Dutch settlers composed a long complaint to the States-General in the Netherlands, seeking help in their struggle against the English, they gave the island special significance: "The ocean on the south, and the East River on the north side of it, shape this island; and as we have said, it is, on account of its good situation, of its land, and of its convenient harbors, and anchoring places, a crown of New Netherland."
But the help was not forthcoming, and in August of 1664, Col. Richard Nicholls, at the head of an English invasion force, made landfall at Gravesend Bay and proclaimed Long Island English territory. Less than two weeks later, Petrus Stuyvesant surrendered New Amsterdam.
More information on Long Island history