The boundaries of each state have a different story. States east of the Appalachian Mountains typically have boundaries based in the original royal land grants, but often those were based on mistaken notions of geography and conjecture about areas not yet known to Europeans. So there are small local disputes over undefined areas, and sometimes those are part of greater 17th- and 18th-century disputes between European nations. Several of the grants purported to run westward all the way to the Pacific, two centuries before anyone knew how far that might be.

After the creation of the United States, state borders were set by Congress—but again, they were often conjecturing that a certain line of latitude would meet a particular mountain range or river in one place, but the geography on the ground proved more complicated. There were often disputes over whether a river boundary meant the ever-changing centerline of the channel, the centerline when originally set, or one shore or another; and disputes over which tributary was the river named in a boundary description. Surveyors sent to mark lines of latitude often made errors of a mile or more.

The details for each state are given in Boundaries of the United States and the Several States, a US Geological Survey booklet available as a PDF here or older versions on archive.org or Google Books. Mark Stein's book How the States Got Their Shapes is a popular book telling the same tales. It's more fun to read, but somehow completely misses any mention of the Washington Meridian, which several Western states' boundaries were set in relation to (rather than the Prime Meridian at Greenwich). Stein also did a follow-up book, How the States Got Their Shapes Too: The People Behind the Borderlines, that tells the human stories of some of the land disputes.