The doctrine by which a person who occupies land they do not own, openly and continuously for the period the state sets, becomes its owner - the elements, the "colour of title" and tax-payment variations, and why it decides fence and driveway disputes far more often than it transfers whole parcels.
Adverse possession converts long possession into ownership. A person who takes possession of another's land and holds it for the statutory period without the owner's permission acquires title to it, and the former owner's right to recover the land is extinguished. The doctrine rests on the statute of limitations for actions to recover land: once the owner's time to sue the possessor has run, the possessor's title is as good as any. Every state recognises it, and the period, which each state sets by statute, varies widely.
The possession must be actual - using the land as an owner would; open and notorious - visible enough that a reasonably attentive owner would notice; exclusive - not shared with the owner or the public; hostile or adverse - without permission, which in most states is judged by the possessor's conduct rather than their state of mind, so a neighbour who honestly believes the strip is theirs qualifies; and continuous for the whole period, though successive possessors may add their periods together. Many states shorten the period or relax the elements for a possessor holding under "colour of title" - a defective deed that purports to convey the land - and a number require that the possessor also have paid the property taxes. Land owned by the government cannot be adversely possessed, and a co-owner's possession is presumed permissive unless they clearly repudiate the others' rights.
In practice the doctrine is invoked over boundary strips: a fence, hedge, driveway, garden or garage that has sat a few feet over the line for decades. A related doctrine, the prescriptive easement, gives a right to continue using another's land - a path, a driveway - on the same elements minus exclusivity, without transferring ownership. A claim is asserted in a quiet-title action and, once established, is confirmed by a judgment recorded in the land records; until then the possessor holds a title that no title company will insure and no buyer can be sure of.
The owner's side is time-critical in the opposite direction from most claims: an owner who discovers a neighbour's encroachment can stop the clock by granting written permission, by demanding removal, or by suing, and the longer nothing is done the closer the neighbour is to owning the strip. The possessor's side needs evidence of every element across the whole period - photographs, aerial images, tax records, testimony of prior owners - and a lawyer to bring the quiet-title action that turns possession into an insurable title. Either party should get a survey before anything else, because a surprising number of these disputes turn out to be about where the line actually is.
Choose your state. Each link opens the directory page for the city in that state with the most currently published law firms in this practice area; a +n beside the city is how many other cities in the state also have one. The list is generated when this page loads, so a state whose listings have lapsed drops out rather than becoming a dead link.